dynamics/c-api/dynamics_8h_source.html

#ifndef DYNAMICS_H_

#define DYNAMICS_H_


#include <complex.h>

#include <stdbool.h>


#define DYN_HYPERBOLIC_FIXED_POINT_SINK 100

#define DYN_HYPERBOLIC_FIXED_POINT_SOURCE 101

#define DYN_HYPERBOLIC_FIXED_POINT_SADDLE 102

#define DYN_NONHYPERBOLIC_FIXED_POINT_UNSTABLE 103

#define DYN_NONHYPERBOLIC_FIXED_POINT_NEUTRALLY_STABLE 104

#define DYN_NONHYPERBOLIC_FIXED_POINT_CENTER 105


#define DYN_REVOLUTE_JOINT 0

#define DYN_PRISMATIC_JOINT 1

#define DYN_FIXED_JOINT 2

#define DYN_CYLINDRICAL_JOINT 3

#define DYN_UNIVERSAL_JOINT 4

#define DYN_SPHERICAL_JOINT 5


#define DYN_FRF_ACCELERANCE_MODEL 1

#define DYN_FRF_RECEPTANCE_MODEL 2


#define DYN_RUNGE_KUTTA_23 10

#define DYN_RUNGE_KUTTA_45 11

#define DYN_RUNGE_KUTTA_853 12

#define DYN_ROSENBROCK 13

#define DYN_BDF 14

#define DYN_ADAMS 15

#define DYN_KENNEDY_CARPENTER_4 16

#define DYN_KENNEDY_CARPENTER_5 17

#define DYN_TSITOURAS_5 18


#define DYN_ACCELERANCE_MODEL 1

#define DYN_RECEPTANCE_MODEL 2


#define DYN_H1 1

#define DYN_H2 2


#define DYN_LEVENBERG_MARQUARDT_UPDATE 1

#define DYN_QUADRATIC_UPDATE 2

#define DYN_NIELSEN_UPDATE 3


#define DYN_POINCARE_TWO_SIDED 0

#define DYN_POINCARE_ONE_SIDED_FROM_FRONT 1

#define DYN_POINCARE_ONE_SIDED_FROM_BACK 2


#define DYN_ONE_POINT_INTEGRATION_RULE 1

#define DYN_TWO_POINT_INTEGRATION_RULE 2

#define DYN_THREE_POINT_INTEGRATION_RULE 3

#define DYN_FOUR_POINT_INTEGRATION_RULE 4

#define DYN_VI_DENSE_SOLVER 1

#define DYN_VI_GRAPH_FACTORIZED_SOLVER 2

#define DYN_VI_FORCE_LEFT_ENDPOINT 1

#define DYN_VI_FORCE_IMPLICIT_ENDPOINT 2

#define DYN_VI_FORCE_MIDPOINT 3


#define DYN_NO_ERROR 0

#define DYN_MEMORY_ERROR 10000

#define DYN_NULL_POINTER_ERROR 10001

#define DYN_INVALID_INPUT_ERROR 10004

#define DYN_MATRIX_SIZE_ERROR 100100

#define DYN_ARRAY_SIZE_ERROR 100105

typedef void (*c_error_handler)(int code, const char *message,

    void *user_data);

typedef void (*c_vecfcn)(int nvar, int neqn, const double *x, double *f,

    void *user_data);

typedef void (*c_modal_excite)(int n, double freq, double complex *f,

    void *user_data);

typedef void (*c_harmonic_ode)(int n, double freq, double t, const double *x,

    double *dxdt, void *user_data);

typedef double (*c_window_function)(int n, int bin, void *user_data);

typedef void (*c_constraint_equations)(int n, int neqn, int nparam,

    const double *xg, const double *fg, const double *xc, const double *p,

    double *fc, void *user_data);

typedef void (*c_ode_fit)(int n, int nparam, const double *mdl, double t,

    const double *x, double F, double *dxdt, void *user_data);


typedef void (*c_ss_excitation)(int n, double t, double *u, void *user_data);


typedef void (*c_ode_equations)(int n, double t, const double *x,

    double *dxdt, void *user_data);


typedef void (*c_poincare_coordinates)(int n, double t, const double *x,

    double coordinates[3], void *user_data);


typedef struct c_variational_state c_variational_state;

typedef void (*c_variational_force)(const c_variational_state *state,

    double *force, double *torque, void *user_data);

typedef void (*c_variational_constraint)(const c_variational_state *state,

    int nconstraint, double *value, void *user_data);

typedef void (*c_variational_constraint_jacobian)(

    const c_variational_state *state, int nconstraint, double *jacobian,

    int ldj, void *user_data);

typedef double (*c_linkage_prescribed_motion)(double t, void *user_data);


typedef struct {

    bool converge_on_chng;

    bool converge_on_fcn;

    bool converge_on_zero_diff;

    int fcn_count;

    int gradient_count;

    int iter_count;

    int jacobian_count;

} c_iteration_behavior;


typedef struct {

    int cycle_count;

    int transient_cycles;

    int points_per_cycle;

    bool frequency_in_hz;

} c_frequency_sweep_controls;


typedef struct {

    double change_in_solution_tolerance;

    double gradient_tolerance;

    double iteration_improvement_tolerance;

    double residual_tolerance;

    int max_function_evaluations;

    int max_iteration_between_updates;

    int max_iteration_count;

} c_iteration_controls;


typedef struct {

    double confidence_interval;

    double probability;

    double standard_error;

    double t_statistic;

} c_regression_statistics;


typedef struct {

    int npts;

    double *input;

    double *output;

    double *t;

} c_dynamic_system_measurement;


typedef struct

{

    double damping_decrease_factor;

    double damping_increase_factor;

    double finite_difference_step_size;

    int method;

} c_lm_solver_options;


typedef struct

{

    double w;

    double x;

    double y;

    double z;

} c_quaternion;


typedef struct

{

    double a;

    double b;

    double c;

    double d;

} c_plane;


typedef struct

{

    double r0[3];

    double v[3];

} c_line;


typedef struct

{

    double u[3];

    double m[3];

} c_plucker_line;


typedef struct

{

    double origin[3];

    double i[3];

    double j[3];

    double k[3];

} c_coordinate_system;


typedef struct

{

    double link_length;

    double link_twist;

    double link_offset;

    double joint_angle;

} c_dh_parameter_set;


typedef struct

{

    int count;

    c_dh_parameter_set *parameters;

} c_dh_table;


typedef struct

{

    double link_length;

    double link_twist;

    double link_offset;

    double joint_angle;

    int joint_type;     // DYN_REVOLUTE_JOINT or DYN_PRISMATIC_JOINT

    double mass;

    double cg[3];

    double inertia[9];  // 3-by-3 matrix in column-major format

} c_binary_link;


typedef struct

{

    int link_count;

    c_binary_link *links;

} c_serial_linkage;


typedef struct

{

    int frame_count;

    double *frames;     // 4-by-4-by-frame_count array in column-major format

    double mass;

    double cg[3];

    double inertia[9];  // 3-by-3 matrix in column-major format

} c_mechanism_link;


typedef struct

{

    int joint_type;     // DYN_REVOLUTE_JOINT, DYN_PRISMATIC_JOINT, etc.

    int parent_link;    // one-based index of the parent link

    int parent_frame;   // one-based index of the frame on the parent link

    int child_link;     // one-based index of the child link

    int child_frame;    // one-based index of the frame on the child link

    bool actuated;

} c_joint;


typedef struct {

    double mass;

    double cg[3];

    double inertia[9];

} c_rigid_body;


struct c_variational_state {

    int body_count;

    double time;

    const double *position;

    const c_quaternion *orientation;

    const double *velocity;

    const double *angular_velocity;

};


typedef struct {

    double tolerance;

    double finite_difference_step;

    double constraint_translation_scale;

    double constraint_rotation_scale;

    int maximum_iterations;

    int maximum_line_search_iterations;

    int linear_solver;

    int force_evaluation;

} c_variational_integrator_settings;


typedef struct {

    double force[3];

    double moment[3];

} c_joint_reaction;


typedef struct {

    int body_1;

    int body_2;

    double point_1[3];

    double point_2[3];

    double stiffness;

    double free_length;

} c_linear_spring;


typedef struct {

    int body_1;

    int body_2;

    double point_1[3];

    double point_2[3];

    double damping;

} c_linear_damper;


typedef struct {

    int joint_index;

    double stiffness;

    double free_angle;

} c_torsional_spring;


typedef struct {

    int joint_index;

    double damping;

} c_torsional_damper;


typedef struct {

    double length;

    double length_rate;

    double force;

} c_axial_element_result;


typedef struct {

    double angle;

    double angle_rate;

    double torque;

} c_torsional_element_result;


typedef void* c_mechanism;

typedef void* c_linkage_dynamic_model;

typedef void* c_structural_integrator;


typedef struct

{

    int order;

    double *coefficients;

} c_polynomial;


typedef struct

{

    c_polynomial numerator;

    c_polynomial denominator;

} c_transfer_function;


typedef struct

{

    int dimension;

    int n_inputs;

    int n_outputs;

    double *A;  // dimension -by- dimension

    double *B;  // dimension -by- n_inputs

    double *C;  // n_outputs -by- dimension

    double *D;  // n_outputs -by- n_inputs

} c_state_space_model;


typedef struct

{

    double density;

    double modulus;

    double poissons_ratio;

} c_material;


typedef struct

{

    int index;

    int dof;

    double x;

    double y;

    double z;

} c_node;


typedef struct

{

    c_material material;

    double area;

    double moment_of_inertia;

    c_node node_1;

    c_node node_2;

} c_beam_element_2d;


typedef struct

{

    c_material material;

    double area;

    double Ixx;

    double Iyy;

    double Izz;

    double Iyz;

    c_node node_1;

    c_node node_2;

    double orientation_point[3];

} c_beam_element_3d;


typedef struct

{

    c_material material;

    double area;

    c_node node_1;

    c_node node_2;

} c_truss_element_2d;


typedef struct

{

    c_material material;

    double area;

    c_node node_1;

    c_node node_2;

} c_truss_element_3d;


typedef struct

{

    double stiffness;

    c_node node_1;

    c_node node_2;

    double direction[2];

    bool use_direction;

} c_spring_element_2d;


typedef struct

{

    double stiffness;

    c_node node_1;

    c_node node_2;

    double direction[3];

    bool use_direction;

} c_spring_element_3d;


typedef struct

{

    double damping_coefficient;

    c_node node_1;

    c_node node_2;

    double direction[2];

    bool use_direction;

} c_damper_element_2d;


typedef struct

{

    double damping_coefficient;

    c_node node_1;

    c_node node_2;

    double direction[3];

    bool use_direction;

} c_damper_element_3d;


typedef struct

{

    double mass;

    c_node node_1;

} c_mass_element_2d;


typedef struct

{

    double mass;

    c_node node_1;

} c_mass_element_3d;


#ifdef __cplusplus

extern "C" {

#endif


void c_set_error_handler(c_error_handler fcn, void *user_data);

int c_get_last_error(void);

int c_get_last_error_message(int n, char *buffer);

void c_clear_error(void);

void c_matmul(int m, int n, int k, double alpha, const double *a, int lda,

    const double *b, int ldb, double beta, double *c, int ldc);


double c_q_factor(double zeta);

double c_estimate_bandwidth(double fn, double zeta);

double c_logarithmic_decrement(double x1, double x2, int n);

double c_damping_from_log_decrement(double delta);

void c_find_free_response_properties(int n, const double *t, const double *x,

    double s, int np, double *delta, double *fn, double *x1, double *x2,

    double *t1, double *t2);

double c_rise_time(double wn, double zeta);

double c_find_settling_amplitude(int n, const double *x);

double c_damping_from_fractional_overshoot(int n, const double *x);

void c_evaluate_step_response(int n, double wn, double zeta, double xs,

    const double *t, double *x);


void c_rotate_x(double angle, double *r, int ldr);

void c_rotate_y(double angle, double *r, int ldr);

void c_rotate_z(double angle, double *r, int ldr);

void c_rotate(const double i[3], const double j[3], const double k[3], double *r,

    int ldr);

void c_acceleration_transform(const double alpha[3], const double omega[3],

    const double a[3], const double x[3], double *r, int ldr);

void c_velocity_transform(const double omega[3], const double v[3],

    const double x[3], double *r, int ldr);


void c_determine_local_stability(int n, const double *a, int lda,

    double complex *ev, int *flag);


void c_dh_forward_kinematics_table(const c_dh_table *tbl, double *T, int ldt);

void c_dh_forward_kinematics(int n, const double *alpha, const double *a,

    const double *theta, const double *d, double *T, int ldt);

void c_dh_forward_kinematics_2(const double *T1, int ldt1, const double *T2,

    int ldt2, double *T, int ldt);

void c_dh_forward_kinematics_3(const double *T1, int ldt1, const double *T2,

    int ldt2, const double *T3, int ldt3, double *T, int ldt);

void c_dh_forward_kinematics_4(const double *T1, int ldt1, const double *T2,

    int ldt2, const double *T3, int ldt3, const double *T4, double *T, int ldt);

void c_dh_forward_kinematics_5(const double *T1, int ldt1, const double *T2,

    int ldt2, const double *T3, int ldt3, const double *T4, int ldt4,

    const double *T5, int ldt5, double *T, int ldt);

void c_dh_forward_kinematics_6(const double *T1, int ldt1, const double *T2,

    int ldt2, const double *T3, int ldt3, const double *T4, int ldt4,

    const double *T5, int ldt5, const double *T6, int ldt6, double *T, int ldt);

void c_dh_forward_kinematics_7(const double *T1, int ldt1, const double *T2,

    int ldt2, const double *T3, int ldt3, const double *T4, int ldt4,

    const double *T5, int ldt5, const double *T6, int ldt6, const double *T7,

    int ldt7, double *T, int ldt);

void c_dh_forward_kinematics_8(const double *T1, int ldt1, const double *T2,

    int ldt2, const double *T3, int ldt3, const double *T4, int ldt4,

    const double *T5, int ldt5, const double *T6, int ldt6, const double *T7,

    int ldt7, const double *T8, int ldt8, double *T, int ldt);

void c_dh_jacobian(int n, const double *alpha, const double *a,

    const double *theta, const double *d, const int *jtypes, double *jac,

    int ldjac);

void c_dh_matrix(double alpha, double a, double theta, double d, double *T,

    int ldt);

void c_dh_rotate_x(double alpha, double *T, int ldt);

void c_dh_rotate_z(double theta, double *T, int ldt);

void c_dh_translate_x(double a, double *T, int ldt);

void c_dh_translate_z(double d, double *T, int ldt);

void c_jacobian_generating_vector(const double *d, const double *k,

    const double *R, int ldr, int jtype, double jvec[6]);

void c_solve_inverse_kinematics(int njoints, int neqn, const c_vecfcn mdl,

    const double *qo, const double *constraints, const double *qmax,

    const double *qmin, double *jvar, double *resid,

    c_iteration_behavior *ib, void *user_data);

void c_to_angle_axis(const double *r, int ldr, double *angle, double axis[3]);

void c_frequency_response(int n, int nfreq, const double *mass, int ldm,

    const double *stiff, int ldk, double alpha, double beta, const double *freq,

    const c_modal_excite frc, double *modes, double *modeshapes, int ldms,

    double complex *rsp, int ldr, void *user_data);

void c_dynamic_stiffness_dense(int n, double omega, const double *mass, int ldm,

    const double *damp, int ldc, const double *stiff, int ldk,

    double complex *dyn_stiff, int ldd);

void c_frf_general_damp_1(int n, int nfreq, const double *mass, int ldm,

    const double *damp, int ldc, const double *stiff, int ldk,

    const double *freq, const c_modal_excite frc, double complex *rsp, int ldr,

    int *ranks, void *user_data);

void c_frf_general_damp_2(int n, int nfreq, double freq1, double freq2,

    const double *mass, int ldm, const double *damp, int ldc,

    const double *stiff, int ldk, const c_modal_excite frc, double complex *rsp,

    int ldr, int *ranks, void *user_data);

double c_compute_modal_damping(double lambda, double alpha, double beta);

double c_chirp(double t, double amp, double span, double f1Hz, double f2Hz);

void c_modal_response(int n, const double *mass, int ldm, const double *stiff,

    int ldk, double *freqs, double *modeshapes, int ldms);

void c_normalize_mode_shapes(int n, double *x, int ldx);

void c_frf_sweep(int n, int nfreq, c_harmonic_ode fcn, const double *freq,

    const double *iv, int solver, double complex *rsp, int ldr,

    const c_frequency_sweep_controls *opts, void *user_data);

void c_set_frequency_sweep_defaults(c_frequency_sweep_controls *x);

void c_evaluate_accelerance_frf_model(int n, int norder, const double *mdl,

    const double *omega, double complex *h);

void c_evaluate_receptance_frf_model(int n, int norder, const double *mdl,

    const double *omega, double complex *h);

void c_set_iteration_controls_defaults(c_iteration_controls *x);

void c_fit_frf(int n, int norder, int method, const double *freq,

    const double complex *rsp, const double *maxp, const double *minp,

    const c_iteration_controls *controls, double *mdl,

    c_regression_statistics *stats);

void c_siso_frequency_response(int n, int nf, const double *x, const double *y,

    double fs, int winsize, c_window_function winfun, int method, double *freq,

    double complex *rsp, void *user_data);


void c_cross_product(const double x[3], const double y[3], double z[3]);

void c_to_skew_symmetric(const double x[3], double *y, int ldy);

double c_vector_angle(const double x[3], const double y[3]);

double c_scalar_projection(const double x[3], const double y[3]);

void c_vector_projection(const double x[3], const double y[3], double z[3]);

double c_vector_magnitude(int n, const double *x);

void c_vector_normalize(int n, double *x);

double c_dot_product(int n, const double *x, const double *y);

bool c_is_symmetric(int m, int n, const double *a, int lda);


void c_siso_model_fit_least_squares(int nsets, int nparams, int neqns,

    const c_ode_fit fcn, const c_dynamic_system_measurement *x,

    const double *ic, double *p, int integrator, int ind, const double *maxp,

    const double *minp, const c_iteration_controls *controls,

    const c_lm_solver_options *opts, int nconstraints, const double *xc,

    const double *yc, const c_constraint_equations constraints, int nweights,

    const double *weights, c_regression_statistics *stats,

    c_iteration_behavior *info, void *user_data);

void c_set_lm_solver_options_defaults(c_lm_solver_options *x);

int c_alloc_dynamic_system_measurement(int n, c_dynamic_system_measurement *x);

void c_free_dynamic_system_measurement(c_dynamic_system_measurement *x);

c_dynamic_system_measurement* c_alloc_dynamic_system_measurement_array(int n,

    const int *ptsper);

void c_free_dynamic_system_measurement_array(int n,

    c_dynamic_system_measurement *x);

void c_quaternion_from_array(const double x[4], c_quaternion *q);

void c_quaternion_from_matrix(const double *x, int ldx, c_quaternion *q);

void c_quaternion_from_angle_axis(double angle, const double axis[3],

    c_quaternion *q);

void c_quaternion_normalize(c_quaternion *q);

void c_quaternion_add(const c_quaternion *x, const c_quaternion *y,

    c_quaternion *q);

void c_quaternion_subtract(const c_quaternion *x, const c_quaternion *y,

    c_quaternion *q);

void c_quaternion_multiply(const c_quaternion *x, const c_quaternion *y,

    c_quaternion *q);

void c_quaternion_divide(const c_quaternion *x, const c_quaternion *y,

    c_quaternion *q);

void c_quaternion_scale(double x, const c_quaternion *y, c_quaternion *q);

void c_quaternion_conjugate(const c_quaternion *q, c_quaternion *qc);

void c_quaternion_rotate(const c_quaternion *q, const double r[3], double rp[3]);

double c_quaternion_abs(const c_quaternion *q);

void c_quaternion_inverse(const c_quaternion *q, c_quaternion *qinv);

void c_quaternion_to_matrix(const c_quaternion *q, double *r, int ldr);

void c_quaternion_to_angle_axis(const c_quaternion *q, double *angle, double axis[3]);

void c_quaternion_exp(const c_quaternion *q, c_quaternion *rst);

void c_quaternion_log(const c_quaternion *q, c_quaternion *rst);

void c_quaternion_pow(const c_quaternion *q, double exponent, c_quaternion *rst);

double c_quaternion_dot_product(const c_quaternion *x, const c_quaternion *y);

void c_quaternion_to_roll_pitch_yaw(const c_quaternion *q, double *roll,

    double *pitch, double *yaw);

void c_plane_normal(const c_plane* pln, double nrm[3]);

void c_plane_from_3_points(const double pt1[3], const double pt2[3],

    const double pt3[3], c_plane *pln);

void c_plane_from_point_and_normal(const double pt[3], const double nrm[3],

    c_plane *pln);

void c_plane_from_points(int n, const double *pts, int ldp, c_plane *pln);

void c_flip_plane_normal(c_plane *pln);

void c_line_from_2_points(const double pt1[3], const double pt2[3], c_line *ln);

void c_line_from_2_planes(const c_plane *p1, const c_plane *p2, c_line *ln);

void c_line_from_points(int n, const double *pts, int ldp, c_line *ln);

void c_evaluate_line_position(const c_line *ln, double t, double x[3]);

bool c_is_parallel_vectors(int n, const double *x, const double *y, double tol);

bool c_is_parallel_lines(const c_line *x, const c_line *y, double tol);

bool c_is_parallel_planes(const c_plane *x, const c_plane *y, double tol);

bool c_is_point_on_plane(const double pt[3], const c_plane *pln, double tol);

bool c_is_point_on_line(const double pt[3], const c_line *ln, double tol);

double c_nearest_point_on_line(const double pt[3], const c_line *ln);

double c_point_to_line_distance(const double pt[3], const c_line *ln);

double c_point_to_plane_distance(const double pt[3], const c_plane *pln);

void c_vector_plane_projection(const double x[3], const c_plane *pln, double px[3]);

void c_point_plane_projection(const double pt[3], const c_plane *pln, double ppt[3]);

void c_plucker_line_from_2_points(const double pt1[3], const double pt2[3],

    c_plucker_line *ln);

void c_plucker_line_from_line(const c_line *src, c_plucker_line *ln);

void c_plucker_line_from_2_planes(const c_plane *p1, const c_plane *p2,

    c_plucker_line *ln);

void c_plucker_line_from_array(const double x[6], c_plucker_line *ln);

void c_plucker_line_mtx_mult(int n, const double *x, int ldx,

    const c_plucker_line *ln, double *y);

void c_plucker_line_to_array(const c_plucker_line *ln, double x[6]);

void c_line_common_normal(const c_line *ln1, const c_line *ln2, c_line *ln);

void c_do_lines_intersect(const c_line *ln1, const c_line *ln2, bool *intersect,

    double *t1, double *t2, double tol);

void c_line_from_point_and_vector(const double pt[3], const double v[3],

    c_line *ln);


void c_poincare_map(int n, const double *x, const double *y, const double *z,

    const c_plane *pln, int side, int nbuffer, double *xbuffer, double *ybuffer,

    double *zbuffer, int *nactual);

void c_poincare_map_ode(c_ode_equations fcn, const double tspan[2], int n,

    const double *iv, int sample_count, const c_plane *pln, int side,

    int solver, c_poincare_coordinates coordinates, int nbuffer,

    double *xbuffer, double *ybuffer, double *zbuffer, int *nactual,

    void *user_data);

int c_alloc_dh_table(int n, c_dh_table *tbl);

void c_free_dh_table(c_dh_table *tbl);

void c_define_link_csys(const double xim1[3], const double zim1[3],

    const double zi[3], const double rim1[3], const double ri[3],

    c_coordinate_system *csys);

void c_define_csys(const double i[3], const double j[3], const double k[3],

    const double o[3], c_coordinate_system *csys);

void c_build_dh_table(int n, const c_coordinate_system *csys, c_dh_table *tbl);


int c_alloc_serial_linkage(int n, c_serial_linkage *lnk);

void c_free_serial_linkage(c_serial_linkage *lnk);

void c_build_serial_linkage(int n, const c_binary_link *links,

    c_serial_linkage *linkage);

void c_serial_linkage_forward_kinematics(int n, const c_serial_linkage *lnk,

    const double *q, double *T, int ldt);

void c_serial_linkage_jacobian(int n, const c_serial_linkage *lnk,

    const double *q, double *jac, int ldj);

void c_serial_linkage_inverse_kinematics(int n, const c_serial_linkage *lnk,

    const double *qo, const double *trg, int ldt, double *q,

    c_iteration_behavior *ib);

int c_alloc_mechanism_link(int nframes, c_mechanism_link *lnk);

void c_free_mechanism_link(c_mechanism_link *lnk);

c_mechanism c_create_parallel_linkage(int nlinks, const c_mechanism_link *links,

    int njoints, const c_joint *joints, int base, int effector,

    const double *tool, int ldt);

c_mechanism c_create_planar_linkage(int nlinks, const c_mechanism_link *links,

    int njoints, const c_joint *joints, int base, int effector,

    const double *tool, int ldt);

void c_free_mechanism(c_mechanism obj);

int c_mechanism_link_count(c_mechanism obj);

int c_mechanism_joint_count(c_mechanism obj);

int c_mechanism_variable_count(c_mechanism obj);

int c_mechanism_loop_count(c_mechanism obj);

int c_mechanism_constraint_count(c_mechanism obj);

int c_mechanism_degrees_of_freedom(c_mechanism obj);

int c_mechanism_actuated_variable_count(c_mechanism obj);

int c_mechanism_space_dimension(c_mechanism obj);

int c_mechanism_link_frame_count(c_mechanism obj, int i);

void c_mechanism_link_frame(c_mechanism obj, int i, int k, double *T, int ldt);

void c_mechanism_get_configuration(c_mechanism obj, int n, double *q);

void c_mechanism_set_configuration(c_mechanism obj, int n, const double *q);

void c_mechanism_body_transform(c_mechanism obj, int i, int n, const double *q,

    double *T, int ldt);

void c_mechanism_end_effector_transform(c_mechanism obj, int n,

    const double *q, double *T, int ldt);

void c_mechanism_constraints(c_mechanism obj, int n, const double *q, int nc,

    double *f);

void c_mechanism_constraint_jacobian(c_mechanism obj, int n, const double *q,

    double *jac, int ldj);

void c_mechanism_solve_configuration(c_mechanism obj, int na, const double *qa,

    int n, double *q, c_iteration_behavior *ib);

void c_mechanism_forward_kinematics(c_mechanism obj, int na, const double *qa,

    double *T, int ldt, c_iteration_behavior *ib);

void c_mechanism_jacobian(c_mechanism obj, int na, const double *qa,

    double *jac, int ldj);

void c_mechanism_inverse_kinematics(c_mechanism obj, const double *trg, int ldt,

    int na, double *qa, c_iteration_behavior *ib);

void c_default_variational_integrator_settings(

    c_variational_integrator_settings *settings);

void c_variational_integrator_solve(int nbody, const c_rigid_body *bodies,

    int ntime, double dt, const double *initial_position,

    const c_quaternion *initial_orientation, const double *initial_velocity,

    const double *initial_angular_velocity, int nconstraint,

    c_variational_force force_callback,

    c_variational_constraint constraint_callback,

    c_variational_constraint_jacobian jacobian_callback, void *user_data,

    const c_variational_integrator_settings *settings, double *position,

    c_quaternion *orientation, double *velocity, double *angular_velocity,

    double *multipliers, int *converged, int *iterations,

    int *jacobian_singular, int *completed_steps);

c_linkage_dynamic_model c_create_serial_linkage_dynamic_model(

    const c_serial_linkage *linkage, int n, const double *q);

c_linkage_dynamic_model c_create_linkage_dynamic_model(bool planar, int nlinks,

    const c_mechanism_link *links, int njoints, const c_joint *joints, int base,

    int nq, const double *q);

void c_free_linkage_dynamic_model(c_linkage_dynamic_model obj);

int c_linkage_dynamic_body_count(c_linkage_dynamic_model obj);

int c_linkage_dynamic_joint_count(c_linkage_dynamic_model obj);

int c_linkage_dynamic_constraint_count(c_linkage_dynamic_model obj);

void c_linkage_dynamic_add_linear_spring(c_linkage_dynamic_model obj,

    const c_linear_spring *element);

void c_linkage_dynamic_add_linear_damper(c_linkage_dynamic_model obj,

    const c_linear_damper *element);

void c_linkage_dynamic_add_torsional_spring(c_linkage_dynamic_model obj,

    const c_torsional_spring *element);

void c_linkage_dynamic_add_torsional_damper(c_linkage_dynamic_model obj,

    const c_torsional_damper *element);

int c_linkage_dynamic_axial_element_count(c_linkage_dynamic_model obj);

int c_linkage_dynamic_torsional_element_count(c_linkage_dynamic_model obj);

void c_linkage_dynamic_axial_element_results(c_linkage_dynamic_model obj,

    int nbody, double time, const double *position,

    const c_quaternion *orientation, const double *velocity,

    const double *angular_velocity, c_axial_element_result *results);

void c_linkage_dynamic_torsional_element_results(c_linkage_dynamic_model obj,

    int nbody, double time, const double *position,

    const c_quaternion *orientation, const double *velocity,

    const double *angular_velocity, c_torsional_element_result *results);

void c_linkage_dynamic_solve(c_linkage_dynamic_model obj, int nbody,

    int nconstraint, const c_variational_integrator_settings *settings,

    int ntime, double dt, const double gravity[3], const double *body_force,

    const double *body_torque, int prescribed_body,

    c_linkage_prescribed_motion prescribed_motion, void *user_data,

    double *position, c_quaternion *orientation, double *velocity,

    double *angular_velocity, double *multipliers, int *converged,

    int *iterations, int *jacobian_singular, int *completed_steps);

void c_linkage_dynamic_joint_reactions(c_linkage_dynamic_model obj, int nbody,

    int nconstraint, double time, const double *position,

    const c_quaternion *orientation, const double *velocity,

    const double *angular_velocity, const double *multipliers,

    c_joint_reaction *reactions);

int c_alloc_polynomial(int order, c_polynomial *p);

void c_free_polynomial(c_polynomial *p);

int c_alloc_transfer_function(int numer_order, int denom_order,

    c_transfer_function *tf);

void c_free_transfer_function(c_transfer_function *tf);

int c_alloc_state_space_model(int dimension, int n_inputs, int n_outputs,

    c_state_space_model *mdl);

void c_free_state_space_model(c_state_space_model *mdl);

void c_evaluate_transfer_function(const c_transfer_function *tf, int n,

    const double complex *s, double complex *z);

void c_transfer_function_poles(const c_transfer_function *tf, int n,

    double complex *p);

void c_transfer_function_zeros(const c_transfer_function *tf, int n,

    double complex *z);

void c_to_ccf_state_space(const c_transfer_function *tf, c_state_space_model *ss);

void c_to_ocf_state_space(const c_transfer_function *tf, c_state_space_model *ss);

void c_create_state_space_model(int n, int n_out, const double *m, int ldm,

    const double *b, int ldb, const double *k, int ldk,

    c_state_space_model *mdl);

void c_create_pid_state_space_model(double kp, double ki, double kd, double tau,

    const c_state_space_model *plant, c_state_space_model *mdl);

void c_transfer_function_multiply(const c_transfer_function *tf1,

    const c_transfer_function *tf2, c_transfer_function *tf);

void c_scale_transfer_function(double x, const c_transfer_function *tf1,

    c_transfer_function *tf);

void c_lti_solve(const c_state_space_model *mdl, const c_ss_excitation u,

    int n, const double *t, int ndof, const double *ic, int solver,

    int nout, double *y, int ldy, void *user_data);

void c_state_space_poles(const c_state_space_model *mdl, int n,

    double complex *p);

void c_state_space_zeros(const c_state_space_model *mdl, int n,

    double complex *z, int *nz);

void c_state_space_transfer_function(const c_state_space_model *mdl, int nin,

    int nout, int n, const double complex *s, double complex *z, int ldz);

double c_beam_element_2d_length(const c_beam_element_2d *elem);

void c_beam_element_2d_stiffness_matrix(const c_beam_element_2d *elem,

    int rule, double *k, int ldk);

void c_beam_element_2d_mass_matrix(const c_beam_element_2d *elem, int rule,

    double *m, int ldm);

void c_beam_element_2d_rotation_matrix(const c_beam_element_2d *elem,

    double *r, int ldr);

void c_beam_element_2d_strain(const c_beam_element_2d *elem,

    const double displacement[6], double s, double strain[2]);

void c_beam_element_2d_stress(const c_beam_element_2d *elem,

    const double displacement[6], double s, double stress[2]);

double c_beam_element_2d_shear_force(const c_beam_element_2d *elem,

    const double displacement[6], double s);

double c_beam_element_2d_bending_moment(const c_beam_element_2d *elem,

    const double displacement[6], double s);

void c_beam_element_2d_external_force_vector(const c_beam_element_2d *elem,

    const double q[2], int rule, double f[6]);

double c_beam_element_3d_length(const c_beam_element_3d *elem);

void c_beam_element_3d_stiffness_matrix(const c_beam_element_3d *elem,

    int rule, double *k, int ldk);

void c_beam_element_3d_mass_matrix(const c_beam_element_3d *elem, int rule,

    double *m, int ldm);

void c_beam_element_3d_rotation_matrix(const c_beam_element_3d *elem,

    double *r, int ldr);

void c_beam_element_3d_strain(const c_beam_element_3d *elem,

    const double displacement[12], double s, double strain[4]);

void c_beam_element_3d_stress(const c_beam_element_3d *elem,

    const double displacement[12], double s, double stress[4]);

void c_beam_element_3d_shear_force(const c_beam_element_3d *elem,

    const double displacement[12], double s, double force[2]);

void c_beam_element_3d_bending_moment(const c_beam_element_3d *elem,

    const double displacement[12], double s, double moment[3]);

void c_beam_element_3d_external_force_vector(const c_beam_element_3d *elem,

    const double q[4], int rule, double f[12]);

void c_assemble_static_system_beam_2d(int gdof, int n,

    const c_beam_element_2d *elements, int nn, const c_node *nodes, int rule,

    double *k, int ldk);

void c_assemble_dynamic_system_beam_2d(int gdof, int n,

    const c_beam_element_2d *elements, int nn, const c_node *nodes, int rule,

    double *m, int ldm, double *k, int ldk);

void c_assemble_static_system_beam_3d(int gdof, int n,

    const c_beam_element_3d *elements, int nn, const c_node *nodes, int rule,

    double *k, int ldk);

void c_assemble_dynamic_system_beam_3d(int gdof, int n,

    const c_beam_element_3d *elements, int nn, const c_node *nodes, int rule,

    double *m, int ldm, double *k, int ldk);

void c_apply_boundary_conditions_mtx(int n, int nbc, int *gdof,

    const double *x, int ldx, double *rst, int ldr);

void c_apply_boundary_conditions_vec(int n, int nbc, int *gdof,

    const double *x, double *rst);

void c_restore_constrained_values_dense(int nred, int nbc, int *gdof,

    const double *x, double *rst);

void c_apply_displacement_constraint_dense(int dof, double val, int n,

    double *k, int ldk, double *f);

void c_solve_static_system_dense(int n, const double *k, int ldk,

    const double *f, double *u);

double c_truss_element_2d_length(const c_truss_element_2d *elem);

void c_truss_element_2d_stiffness_matrix(const c_truss_element_2d *elem,

    double *k, int ldk);

void c_truss_element_2d_mass_matrix(const c_truss_element_2d *elem, int rule,

    double *m, int ldm);

void c_truss_element_2d_rotation_matrix(const c_truss_element_2d *elem,

    double *r, int ldr);

double c_truss_element_2d_strain(const c_truss_element_2d *elem,

    const double displacement[4]);

double c_truss_element_2d_axial_force(const c_truss_element_2d *elem,

    const double displacement[4]);

void c_truss_element_2d_external_force_vector(const c_truss_element_2d *elem,

    const double q[2], int rule, double f[4]);

double c_truss_element_3d_length(const c_truss_element_3d *elem);

void c_truss_element_3d_stiffness_matrix(const c_truss_element_3d *elem,

    double *k, int ldk);

void c_truss_element_3d_mass_matrix(const c_truss_element_3d *elem, int rule,

    double *m, int ldm);

void c_truss_element_3d_rotation_matrix(const c_truss_element_3d *elem,

    double *r, int ldr);

double c_truss_element_3d_strain(const c_truss_element_3d *elem,

    const double displacement[6]);

double c_truss_element_3d_axial_force(const c_truss_element_3d *elem,

    const double displacement[6]);

void c_truss_element_3d_external_force_vector(const c_truss_element_3d *elem,

    const double q[3], int rule, double f[6]);

void c_assemble_static_system_truss_2d(int gdof, int n,

    const c_truss_element_2d *elements, int nn, const c_node *nodes,

    double *k, int ldk);

void c_assemble_dynamic_system_truss_2d(int gdof, int n,

    const c_truss_element_2d *elements, int nn, const c_node *nodes, int rule,

    double *m, int ldm, double *k, int ldk);

void c_assemble_static_system_truss_3d(int gdof, int n,

    const c_truss_element_3d *elements, int nn, const c_node *nodes,

    double *k, int ldk);

void c_assemble_dynamic_system_truss_3d(int gdof, int n,

    const c_truss_element_3d *elements, int nn, const c_node *nodes, int rule,

    double *m, int ldm, double *k, int ldk);

void c_spring_element_2d_stiffness_matrix(const c_spring_element_2d *elem,

    double *k, int ldk);

double c_spring_element_2d_force(const c_spring_element_2d *elem,

    const double displacement[4]);

void c_spring_element_3d_stiffness_matrix(const c_spring_element_3d *elem,

    double *k, int ldk);

double c_spring_element_3d_force(const c_spring_element_3d *elem,

    const double displacement[6]);

void c_damper_element_2d_damping_matrix(const c_damper_element_2d *elem,

    double *c, int ldc);

double c_damper_element_2d_force(const c_damper_element_2d *elem,

    const double velocity[4]);

void c_damper_element_3d_damping_matrix(const c_damper_element_3d *elem,

    double *c, int ldc);

double c_damper_element_3d_force(const c_damper_element_3d *elem,

    const double velocity[6]);

void c_mass_element_2d_mass_matrix(const c_mass_element_2d *elem, double *m,

    int ldm);

void c_mass_element_3d_mass_matrix(const c_mass_element_3d *elem, double *m,

    int ldm);

void c_assemble_discrete_system_2d(int gdof, int nm,

    const c_mass_element_2d *masses, int nd, const c_damper_element_2d *dampers,

    int ns, const c_spring_element_2d *springs, int nn, const c_node *nodes,

    double *m, int ldm, double *c, int ldc, double *k, int ldk);

void c_assemble_discrete_system_3d(int gdof, int nm,

    const c_mass_element_3d *masses, int nd, const c_damper_element_3d *dampers,

    int ns, const c_spring_element_3d *springs, int nn, const c_node *nodes,

    double *m, int ldm, double *c, int ldc, double *k, int ldk);

c_structural_integrator c_create_dense_generalized_alpha_integrator(int n,

    const double *m, int ldm, const double *c, int ldc, const double *k,

    int ldk, double rho_infinity);

void c_free_structural_integrator(c_structural_integrator obj);

void c_structural_integrator_step(c_structural_integrator obj, int n,

    const double *force_current, const double *force_next, double dt,

    double *displacement, double *velocity, double *acceleration);

void c_structural_integrator_solve(c_structural_integrator obj, int n,

    int npts, const double *forces, int ldf, double dt, double *displacement,

    double *velocity, double *acceleration);

#ifdef __cplusplus

}

#endif

#endif


c_variational_force
void(* c_variational_force)(const c_variational_state *state, double *force, double *torque, void *user_data)
External force and torque callback for variational integration.
Definition dynamics.h:335

c_window_function
double(* c_window_function)(int n, int bin, void *user_data)
Window function callback used by SISO frequency analysis.
Definition dynamics.h:262

c_variational_constraint_jacobian
void(* c_variational_constraint_jacobian)(const c_variational_state *state, int nconstraint, double *jacobian, int ldj, void *user_data)
Reduced constraint-Jacobian callback.
Definition dynamics.h:358

c_ss_excitation
void(* c_ss_excitation)(int n, double t, double *u, void *user_data)
State-space input callback used by c_lti_solve.
Definition dynamics.h:299

c_linkage_dynamic_model
void * c_linkage_dynamic_model
Opaque linkage dynamic-model handle.
Definition dynamics.h:896

c_mechanism
void * c_mechanism
Opaque handle to a closed-loop mechanism.
Definition dynamics.h:890

c_ode_fit
void(* c_ode_fit)(int n, int nparam, const double *mdl, double t, const double *x, double F, double *dxdt, void *user_data)
ODE model callback used by system identification.
Definition dynamics.h:289

c_variational_constraint
void(* c_variational_constraint)(const c_variational_state *state, int nconstraint, double *value, void *user_data)
Holonomic constraint callback for variational integration.
Definition dynamics.h:345

c_ode_equations
void(* c_ode_equations)(int n, double t, const double *x, double *dxdt, void *user_data)
Ordinary-differential-equation callback.
Definition dynamics.h:309

c_modal_excite
void(* c_modal_excite)(int n, double freq, double complex *f, void *user_data)
Modal force callback used by frequency-response routines.
Definition dynamics.h:242

c_constraint_equations
void(* c_constraint_equations)(int n, int neqn, int nparam, const double *xg, const double *fg, const double *xc, const double *p, double *fc, void *user_data)
Constraint callback used by least-squares system identification.
Definition dynamics.h:275

c_vecfcn
void(* c_vecfcn)(int nvar, int neqn, const double *x, double *f, void *user_data)
Nonlinear vector function callback.
Definition dynamics.h:233

c_poincare_coordinates
void(* c_poincare_coordinates)(int n, double t, const double *x, double coordinates[3], void *user_data)
Poincare section coordinate callback.
Definition dynamics.h:321

c_linkage_prescribed_motion
double(* c_linkage_prescribed_motion)(double t, void *user_data)
Prescribed planar-link angular motion callback.
Definition dynamics.h:367

c_error_handler
void(* c_error_handler)(int code, const char *message, void *user_data)
Error handler callback.
Definition dynamics.h:223

c_harmonic_ode
void(* c_harmonic_ode)(int n, double freq, double t, const double *x, double *dxdt, void *user_data)
Harmonic ordinary-differential-equation callback.
Definition dynamics.h:253

c_structural_integrator
void * c_structural_integrator
Opaque linear structural time-integrator handle.
Definition dynamics.h:902

c_get_last_error_message
int c_get_last_error_message(int n, char *buffer)
Copy the message for the most recent error on the calling thread.

c_get_last_error
int c_get_last_error(void)
Get the most recent error recorded on the calling thread.

c_set_error_handler
void c_set_error_handler(c_error_handler fcn, void *user_data)
Register a handler invoked whenever the C interface records an error on the calling thread.

c_clear_error
void c_clear_error(void)
Clear the error recorded on the calling thread.

c_vector_projection
void c_vector_projection(const double x[3], const double y[3], double z[3])
Project one vector onto another.

c_scalar_projection
double c_scalar_projection(const double x[3], const double y[3])
Compute the scalar projection of one vector onto another.

c_cross_product
void c_cross_product(const double x[3], const double y[3], double z[3])
Compute the cross product of two three-vectors.

c_normalize_mode_shapes
void c_normalize_mode_shapes(int n, double *x, int ldx)
Normalize mode-shape columns.

c_is_symmetric
bool c_is_symmetric(int m, int n, const double *a, int lda)
Test whether a matrix is symmetric to within a small relative tolerance.

c_siso_model_fit_least_squares
void c_siso_model_fit_least_squares(int nsets, int nparams, int neqns, const c_ode_fit fcn, const c_dynamic_system_measurement *x, const double *ic, double *p, int integrator, int ind, const double *maxp, const double *minp, const c_iteration_controls *controls, const c_lm_solver_options *opts, int nconstraints, const double *xc, const double *yc, const c_constraint_equations constraints, int nweights, const double *weights, c_regression_statistics *stats, c_iteration_behavior *info, void *user_data)
Fit an ODE model to dynamic-system measurements by constrained least squares.

c_alloc_dynamic_system_measurement_array
c_dynamic_system_measurement * c_alloc_dynamic_system_measurement_array(int n, const int *ptsper)
Allocate an array of measurement records.

c_evaluate_accelerance_frf_model
void c_evaluate_accelerance_frf_model(int n, int norder, const double *mdl, const double *omega, double complex *h)
Evaluate an accelerance rational FRF model.

c_set_frequency_sweep_defaults
void c_set_frequency_sweep_defaults(c_frequency_sweep_controls *x)
Fill frequency-sweep controls with defaults.

c_alloc_dynamic_system_measurement
int c_alloc_dynamic_system_measurement(int n, c_dynamic_system_measurement *x)
Allocate one dynamic-system measurement record.

c_vector_magnitude
double c_vector_magnitude(int n, const double *x)
Compute a vector magnitude.

c_to_skew_symmetric
void c_to_skew_symmetric(const double x[3], double *y, int ldy)
Form a skew-symmetric matrix from a three-vector.

c_frequency_response
void c_frequency_response(int n, int nfreq, const double *mass, int ldm, const double *stiff, int ldk, double alpha, double beta, const double *freq, const c_modal_excite frc, double *modes, double *modeshapes, int ldms, double complex *rsp, int ldr, void *user_data)
Compute a modal frequency response for a second-order system.

c_siso_frequency_response
void c_siso_frequency_response(int n, int nf, const double *x, const double *y, double fs, int winsize, c_window_function winfun, int method, double *freq, double complex *rsp, void *user_data)
Estimate a SISO frequency response from input and output records.

c_free_dynamic_system_measurement
void c_free_dynamic_system_measurement(c_dynamic_system_measurement *x)
Release one dynamic-system measurement record.

c_chirp
double c_chirp(double t, double amp, double span, double f1Hz, double f2Hz)
Evaluate a swept-frequency chirp signal.

c_evaluate_receptance_frf_model
void c_evaluate_receptance_frf_model(int n, int norder, const double *mdl, const double *omega, double complex *h)
Evaluate a receptance rational FRF model.

c_fit_frf
void c_fit_frf(int n, int norder, int method, const double *freq, const double complex *rsp, const double *maxp, const double *minp, const c_iteration_controls *controls, double *mdl, c_regression_statistics *stats)
Fit an FRF model to measured data.

c_dynamic_stiffness_dense
void c_dynamic_stiffness_dense(int n, double omega, const double *mass, int ldm, const double *damp, int ldc, const double *stiff, int ldk, double complex *dyn_stiff, int ldd)
Compute dense dynamic stiffness, K - omega^2 M + i omega C.

c_compute_modal_damping
double c_compute_modal_damping(double lambda, double alpha, double beta)
Compute modal damping from Rayleigh coefficients.

c_set_lm_solver_options_defaults
void c_set_lm_solver_options_defaults(c_lm_solver_options *x)
Fill Levenberg-Marquardt options with defaults.

c_frf_general_damp_2
void c_frf_general_damp_2(int n, int nfreq, double freq1, double freq2, const double *mass, int ldm, const double *damp, int ldc, const double *stiff, int ldk, const c_modal_excite frc, double complex *rsp, int ldr, int *ranks, void *user_data)
Compute a general-damping frequency response over an evenly spaced interval.

c_set_iteration_controls_defaults
void c_set_iteration_controls_defaults(c_iteration_controls *x)
Fill nonlinear iteration controls with defaults.

c_free_dynamic_system_measurement_array
void c_free_dynamic_system_measurement_array(int n, c_dynamic_system_measurement *x)
Release an array of measurement records.

c_vector_angle
double c_vector_angle(const double x[3], const double y[3])
Compute the angle between two vectors.

c_frf_general_damp_1
void c_frf_general_damp_1(int n, int nfreq, const double *mass, int ldm, const double *damp, int ldc, const double *stiff, int ldk, const double *freq, const c_modal_excite frc, double complex *rsp, int ldr, int *ranks, void *user_data)
Compute a general-damping frequency response at explicit frequencies.

c_modal_response
void c_modal_response(int n, const double *mass, int ldm, const double *stiff, int ldk, double *freqs, double *modeshapes, int ldms)
Compute modal frequencies and mass-normalized mode shapes.

c_dot_product
double c_dot_product(int n, const double *x, const double *y)
Compute a dot product.

c_vector_normalize
void c_vector_normalize(int n, double *x)
Normalize a vector in place.

c_frf_sweep
void c_frf_sweep(int n, int nfreq, c_harmonic_ode fcn, const double *freq, const double *iv, int solver, double complex *rsp, int ldr, const c_frequency_sweep_controls *opts, void *user_data)
Perform a nonlinear harmonic frequency sweep.

c_plucker_line_from_2_points
void c_plucker_line_from_2_points(const double pt1[3], const double pt2[3], c_plucker_line *ln)
Construct a Pluecker line through two points.

c_point_to_plane_distance
double c_point_to_plane_distance(const double pt[3], const c_plane *pln)
Compute the distance from a point to a plane.

c_point_plane_projection
void c_point_plane_projection(const double pt[3], const c_plane *pln, double ppt[3])
Project a point onto a plane.

c_evaluate_line_position
void c_evaluate_line_position(const c_line *ln, double t, double x[3])
Evaluate a point on a line.

c_do_lines_intersect
void c_do_lines_intersect(const c_line *ln1, const c_line *ln2, bool *intersect, double *t1, double *t2, double tol)
Determine whether two lines intersect and return their parameters.

c_line_from_point_and_vector
void c_line_from_point_and_vector(const double pt[3], const double v[3], c_line *ln)
Construct a line from a point and direction.

c_plucker_line_from_array
void c_plucker_line_from_array(const double x[6], c_plucker_line *ln)
Construct a Pluecker line from six coordinates.

c_plucker_line_from_2_planes
void c_plucker_line_from_2_planes(const c_plane *p1, const c_plane *p2, c_plucker_line *ln)
Construct a Pluecker line from two planes.

c_plucker_line_mtx_mult
void c_plucker_line_mtx_mult(int n, const double *x, int ldx, const c_plucker_line *ln, double *y)
Apply a matrix to a Pluecker line.

c_line_from_points
void c_line_from_points(int n, const double *pts, int ldp, c_line *ln)
Fit a line to point data.

c_point_to_line_distance
double c_point_to_line_distance(const double pt[3], const c_line *ln)
Compute the distance from a point to a line.

c_plane_from_point_and_normal
void c_plane_from_point_and_normal(const double pt[3], const double nrm[3], c_plane *pln)
Construct a plane from a point and normal.

c_vector_plane_projection
void c_vector_plane_projection(const double x[3], const c_plane *pln, double px[3])
Project a vector onto a plane.

c_line_common_normal
void c_line_common_normal(const c_line *ln1, const c_line *ln2, c_line *ln)
Compute the common normal of two lines.

c_is_parallel_lines
bool c_is_parallel_lines(const c_line *x, const c_line *y, double tol)
Test whether two lines are parallel.

c_plane_from_3_points
void c_plane_from_3_points(const double pt1[3], const double pt2[3], const double pt3[3], c_plane *pln)
Construct a plane through three points.

c_flip_plane_normal
void c_flip_plane_normal(c_plane *pln)
Reverse a plane normal and its equation.

c_is_parallel_vectors
bool c_is_parallel_vectors(int n, const double *x, const double *y, double tol)
Test whether two vectors are parallel within a tolerance.

c_poincare_map
void c_poincare_map(int n, const double *x, const double *y, const double *z, const c_plane *pln, int side, int nbuffer, double *xbuffer, double *ybuffer, double *zbuffer, int *nactual)
Compute a Poincare section map from sampled trajectories.

c_poincare_map_ode
void c_poincare_map_ode(c_ode_equations fcn, const double tspan[2], int n, const double *iv, int sample_count, const c_plane *pln, int side, int solver, c_poincare_coordinates coordinates, int nbuffer, double *xbuffer, double *ybuffer, double *zbuffer, int *nactual, void *user_data)
Compute a Poincare section map by integrating an ODE and intersecting uniformly spaced solution sampl...

c_plane_normal
void c_plane_normal(const c_plane *pln, double nrm[3])
Extract a plane normal.

c_is_point_on_line
bool c_is_point_on_line(const double pt[3], const c_line *ln, double tol)
Test whether a point lies on a line.

c_line_from_2_planes
void c_line_from_2_planes(const c_plane *p1, const c_plane *p2, c_line *ln)
Construct the intersection line of two planes.

c_plane_from_points
void c_plane_from_points(int n, const double *pts, int ldp, c_plane *pln)
Fit a plane to point data.

c_nearest_point_on_line
double c_nearest_point_on_line(const double pt[3], const c_line *ln)
Find the parameter of the nearest point on a line.

c_is_parallel_planes
bool c_is_parallel_planes(const c_plane *x, const c_plane *y, double tol)
Test whether two planes are parallel.

c_is_point_on_plane
bool c_is_point_on_plane(const double pt[3], const c_plane *pln, double tol)
Test whether a point lies on a plane.

c_line_from_2_points
void c_line_from_2_points(const double pt1[3], const double pt2[3], c_line *ln)
Construct a line through two points.

c_plucker_line_to_array
void c_plucker_line_to_array(const c_plucker_line *ln, double x[6])
Convert a Pluecker line to six coordinates.

c_plucker_line_from_line
void c_plucker_line_from_line(const c_line *src, c_plucker_line *ln)
Convert a line to Pluecker coordinates.

c_solve_inverse_kinematics
void c_solve_inverse_kinematics(int njoints, int neqn, const c_vecfcn mdl, const double *qo, const double *constraints, const double *qmax, const double *qmin, double *jvar, double *resid, c_iteration_behavior *ib, void *user_data)
Solve a nonlinear inverse-kinematics problem.

c_dh_forward_kinematics_6
void c_dh_forward_kinematics_6(const double *T1, int ldt1, const double *T2, int ldt2, const double *T3, int ldt3, const double *T4, int ldt4, const double *T5, int ldt5, const double *T6, int ldt6, double *T, int ldt)
Multiply six homogeneous transforms.

c_evaluate_step_response
void c_evaluate_step_response(int n, double wn, double zeta, double xs, const double *t, double *x)
Evaluate a second-order step response.

c_dh_forward_kinematics_4
void c_dh_forward_kinematics_4(const double *T1, int ldt1, const double *T2, int ldt2, const double *T3, int ldt3, const double *T4, double *T, int ldt)
Multiply four homogeneous transforms.

c_determine_local_stability
void c_determine_local_stability(int n, const double *a, int lda, double complex *ev, int *flag)
Classify the eigenvalues of a linearized system for local stability.

c_dh_forward_kinematics_7
void c_dh_forward_kinematics_7(const double *T1, int ldt1, const double *T2, int ldt2, const double *T3, int ldt3, const double *T4, int ldt4, const double *T5, int ldt5, const double *T6, int ldt6, const double *T7, int ldt7, double *T, int ldt)
Multiply seven homogeneous transforms.

c_rotate_y
void c_rotate_y(double angle, double *r, int ldr)
Build a rotation matrix about the y axis.

c_dh_translate_z
void c_dh_translate_z(double d, double *T, int ldt)
Build the Denavit-Hartenberg z translation matrix.

c_find_settling_amplitude
double c_find_settling_amplitude(int n, const double *x)
Find the settled response amplitude.

c_dh_matrix
void c_dh_matrix(double alpha, double a, double theta, double d, double *T, int ldt)
Build one Denavit-Hartenberg homogeneous transform.

c_dh_forward_kinematics_2
void c_dh_forward_kinematics_2(const double *T1, int ldt1, const double *T2, int ldt2, double *T, int ldt)
Multiply two homogeneous transforms.

c_estimate_bandwidth
double c_estimate_bandwidth(double fn, double zeta)
Estimate the half-power bandwidth.

c_damping_from_log_decrement
double c_damping_from_log_decrement(double delta)
Convert logarithmic decrement to damping ratio.

c_jacobian_generating_vector
void c_jacobian_generating_vector(const double *d, const double *k, const double *R, int ldr, int jtype, double jvec[6])
Generate one joint Jacobian column.

c_velocity_transform
void c_velocity_transform(const double omega[3], const double v[3], const double x[3], double *r, int ldr)
Build a velocity transformation matrix.

c_dh_jacobian
void c_dh_jacobian(int n, const double *alpha, const double *a, const double *theta, const double *d, const int *jtypes, double *jac, int ldjac)
Compute a Denavit-Hartenberg linkage Jacobian.

c_acceleration_transform
void c_acceleration_transform(const double alpha[3], const double omega[3], const double a[3], const double x[3], double *r, int ldr)
Build an acceleration transformation matrix.

c_matmul
void c_matmul(int m, int n, int k, double alpha, const double *a, int lda, const double *b, int ldb, double beta, double *c, int ldc)
Multiply two column-major matrices: c = alpha*a*b + beta*c.

c_find_free_response_properties
void c_find_free_response_properties(int n, const double *t, const double *x, double s, int np, double *delta, double *fn, double *x1, double *x2, double *t1, double *t2)
Extract damping and frequency properties from a free response.

c_dh_forward_kinematics_3
void c_dh_forward_kinematics_3(const double *T1, int ldt1, const double *T2, int ldt2, const double *T3, int ldt3, double *T, int ldt)
Multiply three homogeneous transforms.

c_dh_rotate_z
void c_dh_rotate_z(double theta, double *T, int ldt)
Build the Denavit-Hartenberg z-axis rotation matrix.

c_dh_forward_kinematics_8
void c_dh_forward_kinematics_8(const double *T1, int ldt1, const double *T2, int ldt2, const double *T3, int ldt3, const double *T4, int ldt4, const double *T5, int ldt5, const double *T6, int ldt6, const double *T7, int ldt7, const double *T8, int ldt8, double *T, int ldt)
Multiply eight homogeneous transforms.

c_rotate_z
void c_rotate_z(double angle, double *r, int ldr)
Build a rotation matrix about the z axis.

c_to_angle_axis
void c_to_angle_axis(const double *r, int ldr, double *angle, double axis[3])
Convert a rotation matrix to angle-axis form.

c_dh_rotate_x
void c_dh_rotate_x(double alpha, double *T, int ldt)
Build the Denavit-Hartenberg x-axis rotation matrix.

c_q_factor
double c_q_factor(double zeta)
Compute the Q factor from a damping ratio.

c_dh_forward_kinematics_5
void c_dh_forward_kinematics_5(const double *T1, int ldt1, const double *T2, int ldt2, const double *T3, int ldt3, const double *T4, int ldt4, const double *T5, int ldt5, double *T, int ldt)
Multiply five homogeneous transforms.

c_dh_forward_kinematics
void c_dh_forward_kinematics(int n, const double *alpha, const double *a, const double *theta, const double *d, double *T, int ldt)
Compute serial Denavit-Hartenberg forward kinematics.

c_dh_translate_x
void c_dh_translate_x(double a, double *T, int ldt)
Build the Denavit-Hartenberg x translation matrix.

c_logarithmic_decrement
double c_logarithmic_decrement(double x1, double x2, int n)
Compute logarithmic decrement from two peaks.

c_rise_time
double c_rise_time(double wn, double zeta)
Compute the 10-to-90 percent rise time.

c_rotate_x
void c_rotate_x(double angle, double *r, int ldr)
Build a rotation matrix about the x axis.

c_damping_from_fractional_overshoot
double c_damping_from_fractional_overshoot(int n, const double *x)
Estimate damping from fractional overshoot.

c_rotate
void c_rotate(const double i[3], const double j[3], const double k[3], double *r, int ldr)
Build a rotation matrix from three basis vectors.

c_dh_forward_kinematics_table
void c_dh_forward_kinematics_table(const c_dh_table *tbl, double *T, int ldt)
Compute forward kinematics from a Denavit-Hartenberg table.

c_mechanism_get_configuration
void c_mechanism_get_configuration(c_mechanism obj, int n, double *q)
Get the current mechanism configuration.

c_mechanism_variable_count
int c_mechanism_variable_count(c_mechanism obj)
Return the number of mechanism variables.

c_free_mechanism
void c_free_mechanism(c_mechanism obj)
Release a mechanism handle.

c_create_parallel_linkage
c_mechanism c_create_parallel_linkage(int nlinks, const c_mechanism_link *links, int njoints, const c_joint *joints, int base, int effector, const double *tool, int ldt)
Create a spatial parallel linkage mechanism.

c_mechanism_jacobian
void c_mechanism_jacobian(c_mechanism obj, int na, const double *qa, double *jac, int ldj)
Evaluate a mechanism Jacobian.

c_mechanism_link_count
int c_mechanism_link_count(c_mechanism obj)
Return the number of links in a mechanism.

c_mechanism_space_dimension
int c_mechanism_space_dimension(c_mechanism obj)
Return the mechanism spatial dimension.

c_mechanism_link_frame
void c_mechanism_link_frame(c_mechanism obj, int i, int k, double *T, int ldt)
Return a link-frame transform.

c_mechanism_actuated_variable_count
int c_mechanism_actuated_variable_count(c_mechanism obj)
Return the number of actuated variables.

c_mechanism_constraint_jacobian
void c_mechanism_constraint_jacobian(c_mechanism obj, int n, const double *q, double *jac, int ldj)
Evaluate the mechanism constraint Jacobian.

c_mechanism_constraint_count
int c_mechanism_constraint_count(c_mechanism obj)
Return the number of constraint equations.

c_mechanism_forward_kinematics
void c_mechanism_forward_kinematics(c_mechanism obj, int na, const double *qa, double *T, int ldt, c_iteration_behavior *ib)
Evaluate forward kinematics for a mechanism.

c_free_mechanism_link
void c_free_mechanism_link(c_mechanism_link *lnk)
Release a multi-frame mechanism link.

c_mechanism_degrees_of_freedom
int c_mechanism_degrees_of_freedom(c_mechanism obj)
Return mechanism degrees of freedom.

c_alloc_mechanism_link
int c_alloc_mechanism_link(int nframes, c_mechanism_link *lnk)
Allocate a multi-frame mechanism link.

c_mechanism_link_frame_count
int c_mechanism_link_frame_count(c_mechanism obj, int i)
Return the frame count for a link.

c_mechanism_solve_configuration
void c_mechanism_solve_configuration(c_mechanism obj, int na, const double *qa, int n, double *q, c_iteration_behavior *ib)
Solve for a complete mechanism configuration.

c_mechanism_set_configuration
void c_mechanism_set_configuration(c_mechanism obj, int n, const double *q)
Set the mechanism configuration.

c_mechanism_body_transform
void c_mechanism_body_transform(c_mechanism obj, int i, int n, const double *q, double *T, int ldt)
Evaluate a body transform at a configuration.

c_mechanism_inverse_kinematics
void c_mechanism_inverse_kinematics(c_mechanism obj, const double *trg, int ldt, int na, double *qa, c_iteration_behavior *ib)
Solve mechanism inverse kinematics.

c_mechanism_constraints
void c_mechanism_constraints(c_mechanism obj, int n, const double *q, int nc, double *f)
Evaluate mechanism constraint equations.

c_mechanism_end_effector_transform
void c_mechanism_end_effector_transform(c_mechanism obj, int n, const double *q, double *T, int ldt)
Evaluate the end-effector transform.

c_mechanism_loop_count
int c_mechanism_loop_count(c_mechanism obj)
Return the number of independent loops.

c_create_planar_linkage
c_mechanism c_create_planar_linkage(int nlinks, const c_mechanism_link *links, int njoints, const c_joint *joints, int base, int effector, const double *tool, int ldt)
Create a planar parallel linkage mechanism.

c_mechanism_joint_count
int c_mechanism_joint_count(c_mechanism obj)
Return the number of joints in a mechanism.

c_quaternion_add
void c_quaternion_add(const c_quaternion *x, const c_quaternion *y, c_quaternion *q)
Add two quaternions.

c_quaternion_divide
void c_quaternion_divide(const c_quaternion *x, const c_quaternion *y, c_quaternion *q)
Divide two quaternions.

c_quaternion_from_matrix
void c_quaternion_from_matrix(const double *x, int ldx, c_quaternion *q)
Construct a quaternion from a rotation matrix.

c_quaternion_abs
double c_quaternion_abs(const c_quaternion *q)
Compute the quaternion norm.

c_quaternion_to_matrix
void c_quaternion_to_matrix(const c_quaternion *q, double *r, int ldr)
Convert a quaternion to a rotation matrix.

c_quaternion_from_array
void c_quaternion_from_array(const double x[4], c_quaternion *q)
Construct a quaternion from four scalar components.

c_quaternion_multiply
void c_quaternion_multiply(const c_quaternion *x, const c_quaternion *y, c_quaternion *q)
Multiply two quaternions.

c_quaternion_to_roll_pitch_yaw
void c_quaternion_to_roll_pitch_yaw(const c_quaternion *q, double *roll, double *pitch, double *yaw)
Convert a quaternion to roll, pitch, and yaw angles.

c_quaternion_exp
void c_quaternion_exp(const c_quaternion *q, c_quaternion *rst)
Compute the quaternion exponential.

c_quaternion_inverse
void c_quaternion_inverse(const c_quaternion *q, c_quaternion *qinv)
Compute a quaternion inverse.

c_quaternion_subtract
void c_quaternion_subtract(const c_quaternion *x, const c_quaternion *y, c_quaternion *q)
Subtract two quaternions.

c_quaternion_log
void c_quaternion_log(const c_quaternion *q, c_quaternion *rst)
Compute the quaternion logarithm.

c_quaternion_dot_product
double c_quaternion_dot_product(const c_quaternion *x, const c_quaternion *y)
Compute the quaternion dot product.

c_quaternion_scale
void c_quaternion_scale(double x, const c_quaternion *y, c_quaternion *q)
Scale a quaternion.

c_quaternion_normalize
void c_quaternion_normalize(c_quaternion *q)
Normalize a quaternion in place.

c_quaternion_conjugate
void c_quaternion_conjugate(const c_quaternion *q, c_quaternion *qc)
Compute a quaternion conjugate.

c_quaternion_rotate
void c_quaternion_rotate(const c_quaternion *q, const double r[3], double rp[3])
Rotate a vector using a quaternion.

c_quaternion_pow
void c_quaternion_pow(const c_quaternion *q, double exponent, c_quaternion *rst)
Raise a quaternion to a real power.

c_quaternion_to_angle_axis
void c_quaternion_to_angle_axis(const c_quaternion *q, double *angle, double axis[3])
Convert a quaternion to angle-axis data.

c_quaternion_from_angle_axis
void c_quaternion_from_angle_axis(double angle, const double axis[3], c_quaternion *q)
Construct a quaternion from angle-axis data.

c_serial_linkage_jacobian
void c_serial_linkage_jacobian(int n, const c_serial_linkage *lnk, const double *q, double *jac, int ldj)
Evaluate the serial-link Jacobian.

c_serial_linkage_forward_kinematics
void c_serial_linkage_forward_kinematics(int n, const c_serial_linkage *lnk, const double *q, double *T, int ldt)
Evaluate serial-link forward kinematics.

c_define_link_csys
void c_define_link_csys(const double xim1[3], const double zim1[3], const double zi[3], const double rim1[3], const double ri[3], c_coordinate_system *csys)
Define a link coordinate system from adjacent geometry.

c_alloc_serial_linkage
int c_alloc_serial_linkage(int n, c_serial_linkage *lnk)
Allocate a serial linkage.

c_free_dh_table
void c_free_dh_table(c_dh_table *tbl)
Release a Denavit-Hartenberg table.

c_alloc_dh_table
int c_alloc_dh_table(int n, c_dh_table *tbl)
Allocate a Denavit-Hartenberg table.

c_build_dh_table
void c_build_dh_table(int n, const c_coordinate_system *csys, c_dh_table *tbl)
Build Denavit-Hartenberg parameters from coordinate systems.

c_build_serial_linkage
void c_build_serial_linkage(int n, const c_binary_link *links, c_serial_linkage *linkage)
Build a serial linkage from link definitions.

c_free_serial_linkage
void c_free_serial_linkage(c_serial_linkage *lnk)
Release a serial linkage.

c_define_csys
void c_define_csys(const double i[3], const double j[3], const double k[3], const double o[3], c_coordinate_system *csys)
Define a coordinate system from basis vectors and origin.

c_serial_linkage_inverse_kinematics
void c_serial_linkage_inverse_kinematics(int n, const c_serial_linkage *lnk, const double *qo, const double *trg, int ldt, double *q, c_iteration_behavior *ib)
Solve serial-link inverse kinematics.

c_free_state_space_model
void c_free_state_space_model(c_state_space_model *mdl)
Release a state-space model.

c_transfer_function_multiply
void c_transfer_function_multiply(const c_transfer_function *tf1, const c_transfer_function *tf2, c_transfer_function *tf)
Multiply two transfer functions.

c_scale_transfer_function
void c_scale_transfer_function(double x, const c_transfer_function *tf1, c_transfer_function *tf)
Scale a transfer function.

c_state_space_poles
void c_state_space_poles(const c_state_space_model *mdl, int n, double complex *p)
Compute state-space poles.

c_alloc_transfer_function
int c_alloc_transfer_function(int numer_order, int denom_order, c_transfer_function *tf)
Allocate a transfer function.

c_state_space_transfer_function
void c_state_space_transfer_function(const c_state_space_model *mdl, int nin, int nout, int n, const double complex *s, double complex *z, int ldz)
Evaluate the state-space transfer matrix.

c_state_space_zeros
void c_state_space_zeros(const c_state_space_model *mdl, int n, double complex *z, int *nz)
Compute state-space zeros.

c_transfer_function_poles
void c_transfer_function_poles(const c_transfer_function *tf, int n, double complex *p)
Compute transfer-function poles.

c_to_ocf_state_space
void c_to_ocf_state_space(const c_transfer_function *tf, c_state_space_model *ss)
Convert a transfer function to observable canonical state space.

c_to_ccf_state_space
void c_to_ccf_state_space(const c_transfer_function *tf, c_state_space_model *ss)
Convert a transfer function to controllable canonical state space.

c_alloc_polynomial
int c_alloc_polynomial(int order, c_polynomial *p)
Allocate a polynomial.

c_free_polynomial
void c_free_polynomial(c_polynomial *p)
Release a polynomial.

c_create_pid_state_space_model
void c_create_pid_state_space_model(double kp, double ki, double kd, double tau, const c_state_space_model *plant, c_state_space_model *mdl)
Create a PID-controlled plant state-space model.

c_create_state_space_model
void c_create_state_space_model(int n, int n_out, const double *m, int ldm, const double *b, int ldb, const double *k, int ldk, c_state_space_model *mdl)
Create a state-space model from mass, damping, and stiffness matrices.

c_transfer_function_zeros
void c_transfer_function_zeros(const c_transfer_function *tf, int n, double complex *z)
Compute transfer-function zeros.

c_evaluate_transfer_function
void c_evaluate_transfer_function(const c_transfer_function *tf, int n, const double complex *s, double complex *z)
Evaluate a transfer function at complex points.

c_free_transfer_function
void c_free_transfer_function(c_transfer_function *tf)
Release a transfer function.

c_alloc_state_space_model
int c_alloc_state_space_model(int dimension, int n_inputs, int n_outputs, c_state_space_model *mdl)
Allocate a continuous state-space model.

c_lti_solve
void c_lti_solve(const c_state_space_model *mdl, const c_ss_excitation u, int n, const double *t, int ndof, const double *ic, int solver, int nout, double *y, int ldy, void *user_data)
Integrate a continuous state-space model.

c_create_dense_generalized_alpha_integrator
c_structural_integrator c_create_dense_generalized_alpha_integrator(int n, const double *m, int ldm, const double *c, int ldc, const double *k, int ldk, double rho_infinity)
Create a dense generalized-alpha integrator for M*a + C*v + K*u = f.

c_structural_integrator_step
void c_structural_integrator_step(c_structural_integrator obj, int n, const double *force_current, const double *force_next, double dt, double *displacement, double *velocity, double *acceleration)
Advance the state by one time step.

c_structural_integrator_solve
void c_structural_integrator_solve(c_structural_integrator obj, int n, int npts, const double *forces, int ldf, double dt, double *displacement, double *velocity, double *acceleration)
Advance the state through a force history using npts - 1 constant steps.

c_free_structural_integrator
void c_free_structural_integrator(c_structural_integrator obj)
Release a structural integrator handle.

c_beam_element_2d_mass_matrix
void c_beam_element_2d_mass_matrix(const c_beam_element_2d *elem, int rule, double *m, int ldm)
Compute the 6-by-6 mass matrix of a 2D beam element.

c_truss_element_2d_stiffness_matrix
void c_truss_element_2d_stiffness_matrix(const c_truss_element_2d *elem, double *k, int ldk)
Compute the 4-by-4 global stiffness matrix of a 2D truss element.

c_truss_element_2d_length
double c_truss_element_2d_length(const c_truss_element_2d *elem)
Compute the length of a 2D truss element.

c_truss_element_3d_mass_matrix
void c_truss_element_3d_mass_matrix(const c_truss_element_3d *elem, int rule, double *m, int ldm)
Compute the 6-by-6 consistent mass matrix of a 3D truss element.

c_mass_element_3d_mass_matrix
void c_mass_element_3d_mass_matrix(const c_mass_element_3d *elem, double *m, int ldm)
Compute the 3-by-3 mass matrix of a 3D point mass element.

c_beam_element_2d_rotation_matrix
void c_beam_element_2d_rotation_matrix(const c_beam_element_2d *elem, double *r, int ldr)
Compute the 6-by-6 rotation matrix of a 2D beam element.

c_damper_element_3d_force
double c_damper_element_3d_force(const c_damper_element_3d *elem, const double velocity[6])
Compute the damper force (positive in tension) in a 3D damper element.

c_assemble_discrete_system_3d
void c_assemble_discrete_system_3d(int gdof, int nm, const c_mass_element_3d *masses, int nd, const c_damper_element_3d *dampers, int ns, const c_spring_element_3d *springs, int nn, const c_node *nodes, double *m, int ldm, double *c, int ldc, double *k, int ldk)
Assemble dense global mass, damping, and stiffness matrices for a 3D system composed of discrete elem...

c_beam_element_2d_shear_force
double c_beam_element_2d_shear_force(const c_beam_element_2d *elem, const double displacement[6], double s)
Compute the local shear force in a 2D beam element at a natural coordinate.

c_beam_element_3d_stress
void c_beam_element_3d_stress(const c_beam_element_3d *elem, const double displacement[12], double s, double stress[4])
Compute the stress in a 3D beam element at a natural coordinate.

c_beam_element_2d_external_force_vector
void c_beam_element_2d_external_force_vector(const c_beam_element_2d *elem, const double q[2], int rule, double f[6])
Compute the equivalent nodal force vector for a distributed load on a 2D beam element.

c_assemble_static_system_truss_2d
void c_assemble_static_system_truss_2d(int gdof, int n, const c_truss_element_2d *elements, int nn, const c_node *nodes, double *k, int ldk)
Assemble a dense global stiffness matrix from 2D truss elements.

c_beam_element_2d_stiffness_matrix
void c_beam_element_2d_stiffness_matrix(const c_beam_element_2d *elem, int rule, double *k, int ldk)
Compute the 6-by-6 stiffness matrix of a 2D beam element.

c_truss_element_3d_strain
double c_truss_element_3d_strain(const c_truss_element_3d *elem, const double displacement[6])
Compute the axial strain in a 3D truss element.

c_beam_element_2d_bending_moment
double c_beam_element_2d_bending_moment(const c_beam_element_2d *elem, const double displacement[6], double s)
Compute the local bending moment in a 2D beam element at a natural coordinate.

c_spring_element_3d_force
double c_spring_element_3d_force(const c_spring_element_3d *elem, const double displacement[6])
Compute the spring force (positive in tension) in a 3D spring element.

c_truss_element_3d_axial_force
double c_truss_element_3d_axial_force(const c_truss_element_3d *elem, const double displacement[6])
Compute the axial force (positive in tension) in a 3D truss element.

c_truss_element_2d_external_force_vector
void c_truss_element_2d_external_force_vector(const c_truss_element_2d *elem, const double q[2], int rule, double f[4])
Compute the equivalent nodal force vector for a distributed load on a 2D truss element.

c_beam_element_3d_bending_moment
void c_beam_element_3d_bending_moment(const c_beam_element_3d *elem, const double displacement[12], double s, double moment[3])
Compute the local moment vector in a 3D beam element at a natural coordinate.

c_assemble_static_system_beam_2d
void c_assemble_static_system_beam_2d(int gdof, int n, const c_beam_element_2d *elements, int nn, const c_node *nodes, int rule, double *k, int ldk)
Assemble a dense global stiffness matrix from 2D beam elements.

c_truss_element_3d_stiffness_matrix
void c_truss_element_3d_stiffness_matrix(const c_truss_element_3d *elem, double *k, int ldk)
Compute the 6-by-6 global stiffness matrix of a 3D truss element.

c_damper_element_3d_damping_matrix
void c_damper_element_3d_damping_matrix(const c_damper_element_3d *elem, double *c, int ldc)
Compute the 6-by-6 global damping matrix of a 3D damper element.

c_solve_static_system_dense
void c_solve_static_system_dense(int n, const double *k, int ldk, const double *f, double *u)
Solve the static system K*u = f for a dense stiffness matrix.

c_beam_element_3d_rotation_matrix
void c_beam_element_3d_rotation_matrix(const c_beam_element_3d *elem, double *r, int ldr)
Compute the 12-by-12 rotation matrix of a 3D beam element.

c_truss_element_3d_length
double c_truss_element_3d_length(const c_truss_element_3d *elem)
Compute the length of a 3D truss element.

c_beam_element_3d_stiffness_matrix
void c_beam_element_3d_stiffness_matrix(const c_beam_element_3d *elem, int rule, double *k, int ldk)
Compute the 12-by-12 stiffness matrix of a 3D beam element.

c_assemble_dynamic_system_truss_2d
void c_assemble_dynamic_system_truss_2d(int gdof, int n, const c_truss_element_2d *elements, int nn, const c_node *nodes, int rule, double *m, int ldm, double *k, int ldk)
Assemble dense global mass and stiffness matrices from 2D truss elements.

c_beam_element_3d_shear_force
void c_beam_element_3d_shear_force(const c_beam_element_3d *elem, const double displacement[12], double s, double force[2])
Compute the local shear-force vector in a 3D beam element at a natural coordinate.

c_beam_element_3d_external_force_vector
void c_beam_element_3d_external_force_vector(const c_beam_element_3d *elem, const double q[4], int rule, double f[12])
Compute the equivalent nodal force vector for a distributed load on a 3D beam element.

c_damper_element_2d_force
double c_damper_element_2d_force(const c_damper_element_2d *elem, const double velocity[4])
Compute the damper force (positive in tension) in a 2D damper element.

c_damper_element_2d_damping_matrix
void c_damper_element_2d_damping_matrix(const c_damper_element_2d *elem, double *c, int ldc)
Compute the 4-by-4 global damping matrix of a 2D damper element.

c_restore_constrained_values_dense
void c_restore_constrained_values_dense(int nred, int nbc, int *gdof, const double *x, double *rst)
Restore the constrained degrees of freedom removed by c_apply_boundary_conditions_vec.

c_truss_element_2d_mass_matrix
void c_truss_element_2d_mass_matrix(const c_truss_element_2d *elem, int rule, double *m, int ldm)
Compute the 4-by-4 consistent mass matrix of a 2D truss element.

c_beam_element_2d_length
double c_beam_element_2d_length(const c_beam_element_2d *elem)
Compute the length of a 2D beam element.

c_assemble_static_system_beam_3d
void c_assemble_static_system_beam_3d(int gdof, int n, const c_beam_element_3d *elements, int nn, const c_node *nodes, int rule, double *k, int ldk)
Assemble a dense global stiffness matrix from 3D beam elements.

c_truss_element_2d_strain
double c_truss_element_2d_strain(const c_truss_element_2d *elem, const double displacement[4])
Compute the axial strain in a 2D truss element.

c_beam_element_3d_mass_matrix
void c_beam_element_3d_mass_matrix(const c_beam_element_3d *elem, int rule, double *m, int ldm)
Compute the 12-by-12 mass matrix of a 3D beam element.

c_assemble_dynamic_system_truss_3d
void c_assemble_dynamic_system_truss_3d(int gdof, int n, const c_truss_element_3d *elements, int nn, const c_node *nodes, int rule, double *m, int ldm, double *k, int ldk)
Assemble dense global mass and stiffness matrices from 3D truss elements.

c_truss_element_2d_axial_force
double c_truss_element_2d_axial_force(const c_truss_element_2d *elem, const double displacement[4])
Compute the axial force (positive in tension) in a 2D truss element.

c_beam_element_3d_strain
void c_beam_element_3d_strain(const c_beam_element_3d *elem, const double displacement[12], double s, double strain[4])
Compute the strain in a 3D beam element at a natural coordinate.

c_spring_element_3d_stiffness_matrix
void c_spring_element_3d_stiffness_matrix(const c_spring_element_3d *elem, double *k, int ldk)
Compute the 6-by-6 global stiffness matrix of a 3D spring element.

c_assemble_dynamic_system_beam_2d
void c_assemble_dynamic_system_beam_2d(int gdof, int n, const c_beam_element_2d *elements, int nn, const c_node *nodes, int rule, double *m, int ldm, double *k, int ldk)
Assemble dense global mass and stiffness matrices from 2D beam elements.

c_mass_element_2d_mass_matrix
void c_mass_element_2d_mass_matrix(const c_mass_element_2d *elem, double *m, int ldm)
Compute the 2-by-2 mass matrix of a 2D point mass element.

c_truss_element_3d_external_force_vector
void c_truss_element_3d_external_force_vector(const c_truss_element_3d *elem, const double q[3], int rule, double f[6])
Compute the equivalent nodal force vector for a distributed load on a 3D truss element.

c_beam_element_2d_strain
void c_beam_element_2d_strain(const c_beam_element_2d *elem, const double displacement[6], double s, double strain[2])
Compute the strain in a 2D beam element at a natural coordinate.

c_assemble_dynamic_system_beam_3d
void c_assemble_dynamic_system_beam_3d(int gdof, int n, const c_beam_element_3d *elements, int nn, const c_node *nodes, int rule, double *m, int ldm, double *k, int ldk)
Assemble dense global mass and stiffness matrices from 3D beam elements.

c_assemble_discrete_system_2d
void c_assemble_discrete_system_2d(int gdof, int nm, const c_mass_element_2d *masses, int nd, const c_damper_element_2d *dampers, int ns, const c_spring_element_2d *springs, int nn, const c_node *nodes, double *m, int ldm, double *c, int ldc, double *k, int ldk)
Assemble dense global mass, damping, and stiffness matrices for a 2D system composed of discrete elem...

c_truss_element_3d_rotation_matrix
void c_truss_element_3d_rotation_matrix(const c_truss_element_3d *elem, double *r, int ldr)
Compute the 6-by-6 rotation matrix of a 3D truss element.

c_spring_element_2d_stiffness_matrix
void c_spring_element_2d_stiffness_matrix(const c_spring_element_2d *elem, double *k, int ldk)
Compute the 4-by-4 global stiffness matrix of a 2D spring element.

c_beam_element_3d_length
double c_beam_element_3d_length(const c_beam_element_3d *elem)
Compute the length of a 3D beam element.

c_beam_element_2d_stress
void c_beam_element_2d_stress(const c_beam_element_2d *elem, const double displacement[6], double s, double stress[2])
Compute the stress in a 2D beam element at a natural coordinate.

c_apply_displacement_constraint_dense
void c_apply_displacement_constraint_dense(int dof, double val, int n, double *k, int ldk, double *f)
Apply a displacement constraint to a single degree of freedom.

c_apply_boundary_conditions_mtx
void c_apply_boundary_conditions_mtx(int n, int nbc, int *gdof, const double *x, int ldx, double *rst, int ldr)
Apply boundary conditions to a dense matrix by removing the constrained rows and columns.

c_apply_boundary_conditions_vec
void c_apply_boundary_conditions_vec(int n, int nbc, int *gdof, const double *x, double *rst)
Apply boundary conditions to a dense vector by removing the constrained entries.

c_truss_element_2d_rotation_matrix
void c_truss_element_2d_rotation_matrix(const c_truss_element_2d *elem, double *r, int ldr)
Compute the 4-by-4 rotation matrix of a 2D truss element.

c_spring_element_2d_force
double c_spring_element_2d_force(const c_spring_element_2d *elem, const double displacement[4])
Compute the spring force (positive in tension) in a 2D spring element.

c_assemble_static_system_truss_3d
void c_assemble_static_system_truss_3d(int gdof, int n, const c_truss_element_3d *elements, int nn, const c_node *nodes, double *k, int ldk)
Assemble a dense global stiffness matrix from 3D truss elements.

c_linkage_dynamic_axial_element_results
void c_linkage_dynamic_axial_element_results(c_linkage_dynamic_model obj, int nbody, double time, const double *position, const c_quaternion *orientation, const double *velocity, const double *angular_velocity, c_axial_element_result *results)
Query all axial elements at one state.

c_linkage_dynamic_add_linear_spring
void c_linkage_dynamic_add_linear_spring(c_linkage_dynamic_model obj, const c_linear_spring *element)
Add a tension/compression linear spring.

c_linkage_dynamic_add_linear_damper
void c_linkage_dynamic_add_linear_damper(c_linkage_dynamic_model obj, const c_linear_damper *element)
Add an axis-only linear viscous damper.

c_linkage_dynamic_constraint_count
int c_linkage_dynamic_constraint_count(c_linkage_dynamic_model obj)
Return the linkage constraint count before any prescribed-motion constraint is added.

c_free_linkage_dynamic_model
void c_free_linkage_dynamic_model(c_linkage_dynamic_model obj)
Release a linkage dynamic-model handle.

c_linkage_dynamic_add_torsional_damper
void c_linkage_dynamic_add_torsional_damper(c_linkage_dynamic_model obj, const c_torsional_damper *element)
Add a twist-rate damper to a revolute joint.

c_default_variational_integrator_settings
void c_default_variational_integrator_settings(c_variational_integrator_settings *settings)
Fill variational-integrator settings with library defaults.

c_linkage_dynamic_solve
void c_linkage_dynamic_solve(c_linkage_dynamic_model obj, int nbody, int nconstraint, const c_variational_integrator_settings *settings, int ntime, double dt, const double gravity[3], const double *body_force, const double *body_torque, int prescribed_body, c_linkage_prescribed_motion prescribed_motion, void *user_data, double *position, c_quaternion *orientation, double *velocity, double *angular_velocity, double *multipliers, int *converged, int *iterations, int *jacobian_singular, int *completed_steps)
Solve linkage dynamics.

c_linkage_dynamic_torsional_element_count
int c_linkage_dynamic_torsional_element_count(c_linkage_dynamic_model obj)

c_linkage_dynamic_add_torsional_spring
void c_linkage_dynamic_add_torsional_spring(c_linkage_dynamic_model obj, const c_torsional_spring *element)
Add a linear torsional spring to a revolute joint.

c_variational_integrator_solve
void c_variational_integrator_solve(int nbody, const c_rigid_body *bodies, int ntime, double dt, const double *initial_position, const c_quaternion *initial_orientation, const double *initial_velocity, const double *initial_angular_velocity, int nconstraint, c_variational_force force_callback, c_variational_constraint constraint_callback, c_variational_constraint_jacobian jacobian_callback, void *user_data, const c_variational_integrator_settings *settings, double *position, c_quaternion *orientation, double *velocity, double *angular_velocity, double *multipliers, int *converged, int *iterations, int *jacobian_singular, int *completed_steps)
Integrate rigid bodies directly in maximal coordinates.

c_linkage_dynamic_axial_element_count
int c_linkage_dynamic_axial_element_count(c_linkage_dynamic_model obj)

c_linkage_dynamic_body_count
int c_linkage_dynamic_body_count(c_linkage_dynamic_model obj)
Return the number of moving rigid bodies in a dynamic model.

c_create_linkage_dynamic_model
c_linkage_dynamic_model c_create_linkage_dynamic_model(bool planar, int nlinks, const c_mechanism_link *links, int njoints, const c_joint *joints, int base, int nq, const double *q)
Create a dynamic model directly from parallel/planar linkage descriptors.

c_create_serial_linkage_dynamic_model
c_linkage_dynamic_model c_create_serial_linkage_dynamic_model(const c_serial_linkage *linkage, int n, const double *q)
Create a dynamic model from a serial linkage value.

c_linkage_dynamic_joint_reactions
void c_linkage_dynamic_joint_reactions(c_linkage_dynamic_model obj, int nbody, int nconstraint, double time, const double *position, const c_quaternion *orientation, const double *velocity, const double *angular_velocity, const double *multipliers, c_joint_reaction *reactions)
Convert one state's linkage multipliers into joint reaction wrenches.

c_linkage_dynamic_torsional_element_results
void c_linkage_dynamic_torsional_element_results(c_linkage_dynamic_model obj, int nbody, double time, const double *position, const c_quaternion *orientation, const double *velocity, const double *angular_velocity, c_torsional_element_result *results)
Query all torsional elements at one state.

c_linkage_dynamic_joint_count
int c_linkage_dynamic_joint_count(c_linkage_dynamic_model obj)
Return the number of joints represented by a dynamic model.

c_axial_element_result
Instantaneous scalar result for an axial force element.
Definition dynamics.h:872

c_axial_element_result::force
double force
Signed force acting on body 1 toward body 2.
Definition dynamics.h:875

c_axial_element_result::length
double length
Current attachment distance.
Definition dynamics.h:873

c_axial_element_result::length_rate
double length_rate
Relative velocity along the element axis.
Definition dynamics.h:874

c_beam_element_2d
A two-dimensional Bernoulli-Euler beam element.
Definition dynamics.h:1021

c_beam_element_2d::material
c_material material
The material.
Definition dynamics.h:1025

c_beam_element_2d::node_1
c_node node_1
The first node of the element (s = -1).
Definition dynamics.h:1037

c_beam_element_2d::moment_of_inertia
double moment_of_inertia
The moment of inertia (second moment of area).
Definition dynamics.h:1033

c_beam_element_2d::area
double area
The cross-sectional area.
Definition dynamics.h:1029

c_beam_element_2d::node_2
c_node node_2
The second node of the element (s = 1).
Definition dynamics.h:1041

c_beam_element_3d
A three-dimensional Bernoulli-Euler beam element.
Definition dynamics.h:1050

c_beam_element_3d::Iyy
double Iyy
The moment of inertia about the element y-axis.
Definition dynamics.h:1066

c_beam_element_3d::node_1
c_node node_1
The first node of the element (s = -1).
Definition dynamics.h:1078

c_beam_element_3d::Iyz
double Iyz
The cross-sectional product of inertia.
Definition dynamics.h:1074

c_beam_element_3d::area
double area
The cross-sectional area.
Definition dynamics.h:1058

c_beam_element_3d::Ixx
double Ixx
The moment of inertia about the element x-axis (torsional).
Definition dynamics.h:1062

c_beam_element_3d::Izz
double Izz
The moment of inertia about the element z-axis.
Definition dynamics.h:1070

c_beam_element_3d::material
c_material material
The material.
Definition dynamics.h:1054

c_beam_element_3d::node_2
c_node node_2
The second node of the element (s = 1).
Definition dynamics.h:1082

c_binary_link
One link in a serial Denavit-Hartenberg linkage.
Definition dynamics.h:669

c_binary_link::link_offset
double link_offset
Link offset.
Definition dynamics.h:681

c_binary_link::joint_angle
double joint_angle
Joint angle or displacement.
Definition dynamics.h:685

c_binary_link::joint_type
int joint_type
Joint type, for example DYN_REVOLUTE_JOINT.
Definition dynamics.h:689

c_binary_link::link_length
double link_length
Link length.
Definition dynamics.h:673

c_binary_link::link_twist
double link_twist
Link twist.
Definition dynamics.h:677

c_binary_link::mass
double mass
Link mass.
Definition dynamics.h:693

c_coordinate_system
An orthonormal coordinate system.
Definition dynamics.h:606

c_damper_element_2d
A two-dimensional linear, axial viscous damper element with x and y translations at each node.
Definition dynamics.h:1205

c_damper_element_2d::use_direction
bool use_direction
True to define the damper axis by direction; false to define it by the vector from node_1 to node_2,...
Definition dynamics.h:1228

c_damper_element_2d::node_1
c_node node_1
The first node of the element.
Definition dynamics.h:1213

c_damper_element_2d::node_2
c_node node_2
The second node of the element.
Definition dynamics.h:1217

c_damper_element_2d::damping_coefficient
double damping_coefficient
The viscous damping coefficient.
Definition dynamics.h:1209

c_damper_element_3d
A three-dimensional linear, axial viscous damper element with x, y, and z translations at each node.
Definition dynamics.h:1236

c_damper_element_3d::damping_coefficient
double damping_coefficient
The viscous damping coefficient.
Definition dynamics.h:1240

c_damper_element_3d::node_1
c_node node_1
The first node of the element.
Definition dynamics.h:1244

c_damper_element_3d::node_2
c_node node_2
The second node of the element.
Definition dynamics.h:1248

c_damper_element_3d::use_direction
bool use_direction
True to define the damper axis by direction; false to define it by the vector from node_1 to node_2,...
Definition dynamics.h:1259

c_dh_parameter_set
One Denavit-Hartenberg parameter set.
Definition dynamics.h:631

c_dh_parameter_set::link_length
double link_length
Link length parameter.
Definition dynamics.h:635

c_dh_parameter_set::joint_angle
double joint_angle
Joint angle parameter.
Definition dynamics.h:647

c_dh_parameter_set::link_twist
double link_twist
Link twist parameter.
Definition dynamics.h:639

c_dh_parameter_set::link_offset
double link_offset
Link offset parameter.
Definition dynamics.h:643

c_dh_table
A dynamically allocated Denavit-Hartenberg table.
Definition dynamics.h:654

c_dh_table::count
int count
Number of parameter sets in the table.
Definition dynamics.h:658

c_dh_table::parameters
c_dh_parameter_set * parameters
Dynamically allocated parameter-set array.
Definition dynamics.h:662

c_dynamic_system_measurement
A single dynamic-system input/output measurement record.
Definition dynamics.h:484

c_dynamic_system_measurement::npts
int npts
Number of samples in the record.
Definition dynamics.h:488

c_dynamic_system_measurement::output
double * output
Output samples.
Definition dynamics.h:496

c_dynamic_system_measurement::input
double * input
Input samples.
Definition dynamics.h:492

c_dynamic_system_measurement::t
double * t
Sample times.
Definition dynamics.h:500

c_frequency_sweep_controls
Controls for a frequency sweep.
Definition dynamics.h:406

c_frequency_sweep_controls::cycle_count
int cycle_count
Number of cycles in the frequency sweep.
Definition dynamics.h:410

c_frequency_sweep_controls::frequency_in_hz
bool frequency_in_hz
True when sweep frequencies are specified in hertz.
Definition dynamics.h:422

c_frequency_sweep_controls::points_per_cycle
int points_per_cycle
Number of frequency points evaluated per cycle.
Definition dynamics.h:418

c_frequency_sweep_controls::transient_cycles
int transient_cycles
Number of initial cycles discarded as transients.
Definition dynamics.h:414

c_iteration_behavior
Iteration statistics returned by nonlinear solver routines.
Definition dynamics.h:372

c_iteration_behavior::jacobian_count
int jacobian_count
Number of Jacobian evaluations.
Definition dynamics.h:400

c_iteration_behavior::iter_count
int iter_count
Number of nonlinear iterations.
Definition dynamics.h:396

c_iteration_behavior::converge_on_chng
bool converge_on_chng
True when convergence was detected from solution changes.
Definition dynamics.h:376

c_iteration_behavior::converge_on_fcn
bool converge_on_fcn
True when convergence was detected from the function value.
Definition dynamics.h:380

c_iteration_behavior::gradient_count
int gradient_count
Number of gradient evaluations.
Definition dynamics.h:392

c_iteration_behavior::converge_on_zero_diff
bool converge_on_zero_diff
True when convergence was detected from a zero difference.
Definition dynamics.h:384

c_iteration_behavior::fcn_count
int fcn_count
Number of function evaluations.
Definition dynamics.h:388

c_iteration_controls
Controls for nonlinear iteration routines.
Definition dynamics.h:428

c_iteration_controls::iteration_improvement_tolerance
double iteration_improvement_tolerance
Minimum improvement required between iterations.
Definition dynamics.h:440

c_iteration_controls::max_function_evaluations
int max_function_evaluations
Maximum number of function evaluations.
Definition dynamics.h:448

c_iteration_controls::residual_tolerance
double residual_tolerance
Convergence tolerance for the residual.
Definition dynamics.h:444

c_iteration_controls::max_iteration_between_updates
int max_iteration_between_updates
Maximum iterations between Jacobian or gradient updates.
Definition dynamics.h:452

c_iteration_controls::change_in_solution_tolerance
double change_in_solution_tolerance
Convergence tolerance for changes in the solution.
Definition dynamics.h:432

c_iteration_controls::gradient_tolerance
double gradient_tolerance
Convergence tolerance for the gradient.
Definition dynamics.h:436

c_iteration_controls::max_iteration_count
int max_iteration_count
Maximum total number of iterations.
Definition dynamics.h:456

c_joint_reaction
World-frame joint reaction exerted on the joint's child link.
Definition dynamics.h:826

c_joint
A joint connecting two mechanism link frames.
Definition dynamics.h:750

c_joint::actuated
bool actuated
Whether the joint variable is actuated.
Definition dynamics.h:774

c_joint::child_frame
int child_frame
One-based child-frame index.
Definition dynamics.h:770

c_joint::parent_link
int parent_link
One-based parent link index.
Definition dynamics.h:758

c_joint::parent_frame
int parent_frame
One-based parent-frame index.
Definition dynamics.h:762

c_joint::child_link
int child_link
One-based child link index.
Definition dynamics.h:766

c_joint::joint_type
int joint_type
Joint type, such as DYN_REVOLUTE_JOINT or DYN_FIXED_JOINT.
Definition dynamics.h:754

c_line
A line represented by a point and direction vector.
Definition dynamics.h:576

c_linear_damper
Axial linear viscous damper between body-fixed points.
Definition dynamics.h:850

c_linear_damper::body_2
int body_2
Second moving-body index, or zero for ground.
Definition dynamics.h:852

c_linear_damper::body_1
int body_1
First moving-body index, or zero for ground.
Definition dynamics.h:851

c_linear_damper::damping
double damping
Axial damping coefficient.
Definition dynamics.h:855

c_linear_spring
Linear spring between body-fixed points; body zero denotes ground.
Definition dynamics.h:834

c_linear_spring::free_length
double free_length
Zero-force length; values below/above this produce compression/tension.
Definition dynamics.h:846

c_linear_spring::body_2
int body_2
Second moving-body index, or zero for ground.
Definition dynamics.h:838

c_linear_spring::body_1
int body_1
First moving-body index, or zero for ground.
Definition dynamics.h:836

c_linear_spring::stiffness
double stiffness
Linear stiffness.
Definition dynamics.h:844

c_lm_solver_options
Options for the Levenberg-Marquardt solver.
Definition dynamics.h:507

c_lm_solver_options::finite_difference_step_size
double finite_difference_step_size
Relative step used for finite-difference derivatives.
Definition dynamics.h:519

c_lm_solver_options::damping_increase_factor
double damping_increase_factor
Factor by which damping is increased after an unsuccessful step.
Definition dynamics.h:515

c_lm_solver_options::damping_decrease_factor
double damping_decrease_factor
Factor by which damping is decreased after a successful step.
Definition dynamics.h:511

c_lm_solver_options::method
int method
Damping update method, such as DYN_LEVENBERG_MARQUARDT_UPDATE.
Definition dynamics.h:523

c_mass_element_2d
A two-dimensional translational point mass element.
Definition dynamics.h:1266

c_mass_element_2d::mass
double mass
The mass.
Definition dynamics.h:1270

c_mass_element_2d::node_1
c_node node_1
The node to which the mass is attached.
Definition dynamics.h:1274

c_mass_element_3d
A three-dimensional translational point mass element.
Definition dynamics.h:1281

c_mass_element_3d::mass
double mass
The mass.
Definition dynamics.h:1285

c_mass_element_3d::node_1
c_node node_1
The node to which the mass is attached.
Definition dynamics.h:1289

c_material
A linear-elastic-isotropic material.
Definition dynamics.h:973

c_material::poissons_ratio
double poissons_ratio
The Poisson's ratio.
Definition dynamics.h:985

c_material::density
double density
The material density.
Definition dynamics.h:977

c_material::modulus
double modulus
The modulus of elasticity.
Definition dynamics.h:981

c_mechanism_link
A multi-frame link used by a closed-loop mechanism.
Definition dynamics.h:723

c_mechanism_link::mass
double mass
Link mass.
Definition dynamics.h:735

c_mechanism_link::frames
double * frames
4-by-4-by-frame_count frame transforms in column-major storage.
Definition dynamics.h:731

c_mechanism_link::frame_count
int frame_count
Number of frames attached to the link.
Definition dynamics.h:727

c_node
A structural node with position and degrees of freedom.
Definition dynamics.h:992

c_node::index
int index
The global index of the node.
Definition dynamics.h:996

c_node::dof
int dof
The number of degrees of freedom associated with the node.
Definition dynamics.h:1000

c_node::x
double x
The x-coordinate.
Definition dynamics.h:1004

c_node::y
double y
The y-coordinate.
Definition dynamics.h:1008

c_node::z
double z
The z-coordinate.
Definition dynamics.h:1012

c_plane
Plane coefficients satisfying a*x + b*y + c*z + d = 0.
Definition dynamics.h:553

c_plane::a
double a
Coefficient of x in the plane equation.
Definition dynamics.h:557

c_plane::d
double d
Constant plane coefficient.
Definition dynamics.h:569

c_plane::c
double c
Coefficient of z in the plane equation.
Definition dynamics.h:565

c_plane::b
double b
Coefficient of y in the plane equation.
Definition dynamics.h:561

c_plucker_line
A Pluecker line represented by direction and moment vectors.
Definition dynamics.h:591

c_polynomial
A polynomial with dynamically allocated coefficients.
Definition dynamics.h:908

c_polynomial::order
int order
Polynomial order.
Definition dynamics.h:912

c_polynomial::coefficients
double * coefficients
Coefficients in ascending order of power.
Definition dynamics.h:916

c_quaternion
A quaternion stored as scalar component followed by vector terms.
Definition dynamics.h:530

c_quaternion::x
double x
First vector quaternion component.
Definition dynamics.h:538

c_quaternion::y
double y
Second vector quaternion component.
Definition dynamics.h:542

c_quaternion::z
double z
Third vector quaternion component.
Definition dynamics.h:546

c_quaternion::w
double w
Scalar quaternion component.
Definition dynamics.h:534

c_regression_statistics
Regression statistics returned by fitting routines.
Definition dynamics.h:462

c_regression_statistics::standard_error
double standard_error
Standard error of the fitted parameter.
Definition dynamics.h:474

c_regression_statistics::t_statistic
double t_statistic
Student t statistic for the fitted parameter.
Definition dynamics.h:478

c_regression_statistics::probability
double probability
Probability associated with the fitted parameter statistic.
Definition dynamics.h:470

c_regression_statistics::confidence_interval
double confidence_interval
Width of the confidence interval for a fitted parameter.
Definition dynamics.h:466

c_rigid_body
Rigid-body mass properties for direct variational integration.
Definition dynamics.h:778

c_rigid_body::mass
double mass
Body mass.
Definition dynamics.h:780

c_serial_linkage
A serial linkage and its link array.
Definition dynamics.h:708

c_serial_linkage::link_count
int link_count
Number of links.
Definition dynamics.h:712

c_serial_linkage::links
c_binary_link * links
Link array.
Definition dynamics.h:716

c_spring_element_2d
A two-dimensional linear, axial spring element with x and y translations at each node.
Definition dynamics.h:1143

c_spring_element_2d::node_1
c_node node_1
The first node of the element.
Definition dynamics.h:1151

c_spring_element_2d::stiffness
double stiffness
The spring stiffness.
Definition dynamics.h:1147

c_spring_element_2d::node_2
c_node node_2
The second node of the element.
Definition dynamics.h:1155

c_spring_element_2d::use_direction
bool use_direction
True to define the spring axis by direction; false to define it by the vector from node_1 to node_2,...
Definition dynamics.h:1166

c_spring_element_3d
A three-dimensional linear, axial spring element with x, y, and z translations at each node.
Definition dynamics.h:1174

c_spring_element_3d::node_2
c_node node_2
The second node of the element.
Definition dynamics.h:1186

c_spring_element_3d::node_1
c_node node_1
The first node of the element.
Definition dynamics.h:1182

c_spring_element_3d::stiffness
double stiffness
The spring stiffness.
Definition dynamics.h:1178

c_spring_element_3d::use_direction
bool use_direction
True to define the spring axis by direction; false to define it by the vector from node_1 to node_2,...
Definition dynamics.h:1197

c_state_space_model
A continuous state-space model with column-major matrices.
Definition dynamics.h:938

c_state_space_model::A
double * A
State matrix, dimension by dimension.
Definition dynamics.h:954

c_state_space_model::n_outputs
int n_outputs
Number of outputs.
Definition dynamics.h:950

c_state_space_model::dimension
int dimension
Number of state variables.
Definition dynamics.h:942

c_state_space_model::D
double * D
Feedthrough matrix, n_outputs by n_inputs.
Definition dynamics.h:966

c_state_space_model::B
double * B
Input matrix, dimension by n_inputs.
Definition dynamics.h:958

c_state_space_model::n_inputs
int n_inputs
Number of inputs.
Definition dynamics.h:946

c_state_space_model::C
double * C
Output matrix, n_outputs by dimension.
Definition dynamics.h:962

c_torsional_damper
Twist-rate damper bound to a revolute-joint axis.
Definition dynamics.h:866

c_torsional_damper::joint_index
int joint_index
One-based revolute-joint index.
Definition dynamics.h:867

c_torsional_damper::damping
double damping
Torque per unit relative angular velocity.
Definition dynamics.h:868

c_torsional_element_result
Instantaneous scalar result for a torsional force element.
Definition dynamics.h:879

c_torsional_element_result::torque
double torque
Signed torque acting on the child link.
Definition dynamics.h:882

c_torsional_element_result::angle
double angle
Signed relative revolute-joint angle in radians.
Definition dynamics.h:880

c_torsional_element_result::angle_rate
double angle_rate
Relative twist rate about the joint axis.
Definition dynamics.h:881

c_torsional_spring
Linear torsional spring bound to a revolute-joint axis.
Definition dynamics.h:859

c_torsional_spring::joint_index
int joint_index
One-based revolute-joint index.
Definition dynamics.h:860

c_torsional_spring::stiffness
double stiffness
Torque per radian.
Definition dynamics.h:861

c_torsional_spring::free_angle
double free_angle
Zero-torque relative joint angle in radians.
Definition dynamics.h:862

c_transfer_function
A numerator/denominator transfer-function pair.
Definition dynamics.h:923

c_transfer_function::denominator
c_polynomial denominator
Denominator polynomial.
Definition dynamics.h:931

c_transfer_function::numerator
c_polynomial numerator
Numerator polynomial.
Definition dynamics.h:927

c_truss_element_2d
A two-dimensional, pin-jointed, axial-only truss element with x and y translations at each node.
Definition dynamics.h:1095

c_truss_element_2d::area
double area
The cross-sectional area.
Definition dynamics.h:1103

c_truss_element_2d::node_2
c_node node_2
The second node of the element (s = 1).
Definition dynamics.h:1111

c_truss_element_2d::node_1
c_node node_1
The first node of the element (s = -1).
Definition dynamics.h:1107

c_truss_element_2d::material
c_material material
The material.
Definition dynamics.h:1099

c_truss_element_3d
A three-dimensional, pin-jointed, axial-only truss element with x, y, and z translations at each node...
Definition dynamics.h:1119

c_truss_element_3d::material
c_material material
The material.
Definition dynamics.h:1123

c_truss_element_3d::node_1
c_node node_1
The first node of the element (s = -1).
Definition dynamics.h:1131

c_truss_element_3d::area
double area
The cross-sectional area.
Definition dynamics.h:1127

c_truss_element_3d::node_2
c_node node_2
The second node of the element (s = 1).
Definition dynamics.h:1135

c_variational_integrator_settings
Numerical controls for the maximal-coordinate variational integrator.
Definition dynamics.h:804

c_variational_integrator_settings::tolerance
double tolerance
Euclidean nonlinear-residual convergence tolerance.
Definition dynamics.h:806

c_variational_integrator_settings::finite_difference_step
double finite_difference_step
Relative forward-difference step used for numerical Jacobians.
Definition dynamics.h:808

c_variational_integrator_settings::maximum_line_search_iterations
int maximum_line_search_iterations
Maximum residual line-search step halvings per Newton iteration.
Definition dynamics.h:816

c_variational_integrator_settings::constraint_rotation_scale
double constraint_rotation_scale
Dimensionless quaternion-tangent finite-difference scale.
Definition dynamics.h:812

c_variational_integrator_settings::maximum_iterations
int maximum_iterations
Maximum Newton iterations allowed per time step.
Definition dynamics.h:814

c_variational_integrator_settings::linear_solver
int linear_solver
DYN_VI_DENSE_SOLVER or DYN_VI_GRAPH_FACTORIZED_SOLVER.
Definition dynamics.h:818

c_variational_integrator_settings::constraint_translation_scale
double constraint_translation_scale
Translation scale used as the absolute finite-difference floor.
Definition dynamics.h:810

c_variational_integrator_settings::force_evaluation
int force_evaluation
One of DYN_VI_FORCE_LEFT_ENDPOINT, DYN_VI_FORCE_IMPLICIT_ENDPOINT, or DYN_VI_FORCE_MIDPOINT.
Definition dynamics.h:822

c_variational_state
A non-owning view of one maximal-coordinate callback state.
Definition dynamics.h:788

c_variational_state::time
double time
Simulation time associated with the state.
Definition dynamics.h:792

c_variational_state::position
const double * position
World-frame center-of-mass positions, shape 3-by-body_count.
Definition dynamics.h:794

c_variational_state::orientation
const c_quaternion * orientation
Body-to-world unit quaternions, length body_count.
Definition dynamics.h:796

c_variational_state::velocity
const double * velocity
World-frame center-of-mass velocities, shape 3-by-body_count.
Definition dynamics.h:798

c_variational_state::angular_velocity
const double * angular_velocity
Body-frame angular velocities, shape 3-by-body_count.
Definition dynamics.h:800

c_variational_state::body_count
int body_count
Number of rigid bodies represented by the state.
Definition dynamics.h:790