dynamics.h File Reference

Public C interface to the DYNAMICS library. More...

#include <complex.h>
#include <stdbool.h>

Go to the source code of this file.

Classes
struct	c_iteration_behavior
	Iteration statistics returned by nonlinear solver routines. More...
struct	c_frequency_sweep_controls
	Controls for a frequency sweep. More...
struct	c_iteration_controls
	Controls for nonlinear iteration routines. More...
struct	c_regression_statistics
	Regression statistics returned by fitting routines. More...
struct	c_dynamic_system_measurement
	A single dynamic-system input/output measurement record. More...
struct	c_lm_solver_options
	Options for the Levenberg-Marquardt solver. More...
struct	c_quaternion
	A quaternion stored as scalar component followed by vector terms. More...
struct	c_plane
	Plane coefficients satisfying a*x + b*y + c*z + d = 0. More...
struct	c_line
	A line represented by a point and direction vector. More...
struct	c_plucker_line
	A Pluecker line represented by direction and moment vectors. More...
struct	c_coordinate_system
	An orthonormal coordinate system. More...
struct	c_dh_parameter_set
	One Denavit-Hartenberg parameter set. More...
struct	c_dh_table
	A dynamically allocated Denavit-Hartenberg table. More...
struct	c_binary_link
	One link in a serial Denavit-Hartenberg linkage. More...
struct	c_serial_linkage
	A serial linkage and its link array. More...
struct	c_mechanism_link
	A multi-frame link used by a closed-loop mechanism. More...
struct	c_joint
	A joint connecting two mechanism link frames. More...
struct	c_rigid_body
	Rigid-body mass properties for direct variational integration. More...
struct	c_variational_state
	A non-owning view of one maximal-coordinate callback state. More...
struct	c_variational_integrator_settings
	Numerical controls for the maximal-coordinate variational integrator. More...
struct	c_joint_reaction
	World-frame joint reaction exerted on the joint's child link. More...
struct	c_linear_spring
	Linear spring between body-fixed points; body zero denotes ground. More...
struct	c_linear_damper
	Axial linear viscous damper between body-fixed points. More...
struct	c_torsional_spring
	Linear torsional spring bound to a revolute-joint axis. More...
struct	c_torsional_damper
	Twist-rate damper bound to a revolute-joint axis. More...
struct	c_axial_element_result
	Instantaneous scalar result for an axial force element. More...
struct	c_torsional_element_result
	Instantaneous scalar result for a torsional force element. More...
struct	c_polynomial
	A polynomial with dynamically allocated coefficients. More...
struct	c_transfer_function
	A numerator/denominator transfer-function pair. More...
struct	c_state_space_model
	A continuous state-space model with column-major matrices. More...
struct	c_material
	A linear-elastic-isotropic material. More...
struct	c_node
	A structural node with position and degrees of freedom. More...
struct	c_beam_element_2d
	A two-dimensional Bernoulli-Euler beam element. More...
struct	c_beam_element_3d
	A three-dimensional Bernoulli-Euler beam element. More...
struct	c_truss_element_2d
	A two-dimensional, pin-jointed, axial-only truss element with x and y translations at each node. More...
struct	c_truss_element_3d
	A three-dimensional, pin-jointed, axial-only truss element with x, y, and z translations at each node. More...
struct	c_spring_element_2d
	A two-dimensional linear, axial spring element with x and y translations at each node. More...
struct	c_spring_element_3d
	A three-dimensional linear, axial spring element with x, y, and z translations at each node. More...
struct	c_damper_element_2d
	A two-dimensional linear, axial viscous damper element with x and y translations at each node. More...
struct	c_damper_element_3d
	A three-dimensional linear, axial viscous damper element with x, y, and z translations at each node. More...
struct	c_mass_element_2d
	A two-dimensional translational point mass element. More...
struct	c_mass_element_3d
	A three-dimensional translational point mass element. More...

Macros
#define	DYN_HYPERBOLIC_FIXED_POINT_SINK   100
	Hyperbolic fixed point classified as a sink.
#define	DYN_HYPERBOLIC_FIXED_POINT_SOURCE   101
	Hyperbolic fixed point classified as a source.
#define	DYN_HYPERBOLIC_FIXED_POINT_SADDLE   102
	Hyperbolic fixed point classified as a saddle.
#define	DYN_NONHYPERBOLIC_FIXED_POINT_UNSTABLE   103
	Nonhyperbolic fixed point classified as unstable.
#define	DYN_NONHYPERBOLIC_FIXED_POINT_NEUTRALLY_STABLE   104
	Nonhyperbolic fixed point classified as neutrally stable.
#define	DYN_NONHYPERBOLIC_FIXED_POINT_CENTER   105
	Nonhyperbolic fixed point classified as a center.
#define	DYN_REVOLUTE_JOINT   0
	Revolute joint type.
#define	DYN_PRISMATIC_JOINT   1
	Prismatic joint type.
#define	DYN_FIXED_JOINT   2
	Fixed joint type.
#define	DYN_CYLINDRICAL_JOINT   3
	Cylindrical joint type.
#define	DYN_UNIVERSAL_JOINT   4
	Universal joint type.
#define	DYN_SPHERICAL_JOINT   5
	Spherical joint type.
#define	DYN_FRF_ACCELERANCE_MODEL   1
	Frequency-response model expressed as accelerance.
#define	DYN_FRF_RECEPTANCE_MODEL   2
	Frequency-response model expressed as receptance.
#define	DYN_RUNGE_KUTTA_23   10
	Runge-Kutta 2/3 integration method.
#define	DYN_RUNGE_KUTTA_45   11
	Runge-Kutta 4/5 integration method.
#define	DYN_RUNGE_KUTTA_853   12
	Runge-Kutta 8/5/3 integration method.
#define	DYN_ROSENBROCK   13
	Rosenbrock integration method.
#define	DYN_BDF   14
	Backward-differentiation-formula integration method.
#define	DYN_ADAMS   15
	Adams integration method.
#define	DYN_KENNEDY_CARPENTER_4   16
	Kennedy-Carpenter fourth-order integration method.
#define	DYN_KENNEDY_CARPENTER_5   17
	Kennedy-Carpenter fifth-order integration method.
#define	DYN_TSITOURAS_5   18
	Tsitouras fifth-order integration method.
#define	DYN_ACCELERANCE_MODEL   1
	Accelerance model selector for system identification.
#define	DYN_RECEPTANCE_MODEL   2
	Receptance model selector for system identification.
#define	DYN_H1   1
	H1 estimator selector for SISO frequency analysis.
#define	DYN_H2   2
	H2 estimator selector for SISO frequency analysis.
#define	DYN_LEVENBERG_MARQUARDT_UPDATE   1
	Levenberg-Marquardt damping update method.
#define	DYN_QUADRATIC_UPDATE   2
	Quadratic damping update method.
#define	DYN_NIELSEN_UPDATE   3
	Nielsen damping update method.
#define	DYN_POINCARE_TWO_SIDED   0
	Store intersections with both directions of the Poincare plane.
#define	DYN_POINCARE_ONE_SIDED_FROM_FRONT   1
	Store intersections approaching the Poincare plane from the front.
#define	DYN_POINCARE_ONE_SIDED_FROM_BACK   2
	Store intersections approaching the Poincare plane from the back.
#define	DYN_ONE_POINT_INTEGRATION_RULE   1
	Single-point Gauss integration rule.
#define	DYN_TWO_POINT_INTEGRATION_RULE   2
	Two-point Gauss integration rule.
#define	DYN_THREE_POINT_INTEGRATION_RULE   3
	Three-point Gauss integration rule.
#define	DYN_FOUR_POINT_INTEGRATION_RULE   4
	Four-point Gauss integration rule.
#define	DYN_VI_DENSE_SOLVER   1
	Dense LU solver for variational-integrator Newton systems.
#define	DYN_VI_GRAPH_FACTORIZED_SOLVER   2
	Graph-factorized solver for variational-integrator Newton systems.
#define	DYN_VI_FORCE_LEFT_ENDPOINT   1
	Evaluate applied loads at the current state (explicit left endpoint).
#define	DYN_VI_FORCE_IMPLICIT_ENDPOINT   2
	Evaluate applied loads at the trial next state inside Newton.
#define	DYN_VI_FORCE_MIDPOINT   3
	Evaluate applied loads at an interpolated midpoint state inside Newton.
#define	DYN_NO_ERROR   0
	No error has been recorded.
#define	DYN_MEMORY_ERROR   10000
	A memory allocation failed.
#define	DYN_NULL_POINTER_ERROR   10001
	A required pointer or handle was NULL or invalid.
#define	DYN_INVALID_INPUT_ERROR   10004
	An input argument was invalid.
#define	DYN_MATRIX_SIZE_ERROR   100100
	A matrix was incorrectly sized.
#define	DYN_ARRAY_SIZE_ERROR   100105
	An array was incorrectly sized.

Typedefs
typedef void(*	c_error_handler) (int code, const char *message, void *user_data)
	Error handler callback.
typedef void(*	c_vecfcn) (int nvar, int neqn, const double *x, double *f, void *user_data)
	Nonlinear vector function callback.
typedef void(*	c_modal_excite) (int n, double freq, double complex *f, void *user_data)
	Modal force callback used by frequency-response routines.
typedef void(*	c_harmonic_ode) (int n, double freq, double t, const double *x, double *dxdt, void *user_data)
	Harmonic ordinary-differential-equation callback.
typedef double(*	c_window_function) (int n, int bin, void *user_data)
	Window function callback used by SISO frequency analysis.
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)
	Constraint callback used by least-squares system identification.
typedef 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.
typedef void(*	c_ss_excitation) (int n, double t, double *u, void *user_data)
	State-space input callback used by c_lti_solve.
typedef void(*	c_ode_equations) (int n, double t, const double *x, double *dxdt, void *user_data)
	Ordinary-differential-equation callback.
typedef void(*	c_poincare_coordinates) (int n, double t, const double *x, double coordinates[3], void *user_data)
	Poincare section coordinate callback.
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)
	External force and torque callback for variational integration.
typedef void(*	c_variational_constraint) (const c_variational_state *state, int nconstraint, double *value, void *user_data)
	Holonomic constraint callback for variational integration.
typedef void(*	c_variational_constraint_jacobian) (const c_variational_state *state, int nconstraint, double *jacobian, int ldj, void *user_data)
	Reduced constraint-Jacobian callback.
typedef double(*	c_linkage_prescribed_motion) (double t, void *user_data)
	Prescribed planar-link angular motion callback.
typedef void *	c_mechanism
	Opaque handle to a closed-loop mechanism.
typedef void *	c_linkage_dynamic_model
	Opaque linkage dynamic-model handle.
typedef void *	c_structural_integrator
	Opaque linear structural time-integrator handle.

Functions
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.
int	c_get_last_error (void)
	Get the most recent error recorded on the calling thread.
int	c_get_last_error_message (int n, char *buffer)
	Copy the message for the most recent error on the calling thread.
void	c_clear_error (void)
	Clear the error recorded on the calling thread.
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.
double	c_q_factor (double zeta)
	Compute the Q factor from a damping ratio.
double	c_estimate_bandwidth (double fn, double zeta)
	Estimate the half-power bandwidth.
double	c_logarithmic_decrement (double x1, double x2, int n)
	Compute logarithmic decrement from two peaks.
double	c_damping_from_log_decrement (double delta)
	Convert logarithmic decrement to damping ratio.
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.
double	c_rise_time (double wn, double zeta)
	Compute the 10-to-90 percent rise time.
double	c_find_settling_amplitude (int n, const double *x)
	Find the settled response amplitude.
double	c_damping_from_fractional_overshoot (int n, const double *x)
	Estimate damping from fractional overshoot.
void	c_evaluate_step_response (int n, double wn, double zeta, double xs, const double *t, double *x)
	Evaluate a second-order step response.
void	c_rotate_x (double angle, double *r, int ldr)
	Build a rotation matrix about the x axis.
void	c_rotate_y (double angle, double *r, int ldr)
	Build a rotation matrix about the y axis.
void	c_rotate_z (double angle, double *r, int ldr)
	Build a rotation matrix about the z axis.
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.
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.
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.
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.
void	c_dh_forward_kinematics_table (const c_dh_table *tbl, double *T, int ldt)
	Compute forward kinematics from a Denavit-Hartenberg table.
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.
void	c_dh_forward_kinematics_2 (const double *T1, int ldt1, const double *T2, int ldt2, double *T, int ldt)
	Multiply two homogeneous transforms.
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.
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.
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.
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.
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.
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.
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.
void	c_dh_matrix (double alpha, double a, double theta, double d, double *T, int ldt)
	Build one Denavit-Hartenberg homogeneous transform.
void	c_dh_rotate_x (double alpha, double *T, int ldt)
	Build the Denavit-Hartenberg x-axis rotation matrix.
void	c_dh_rotate_z (double theta, double *T, int ldt)
	Build the Denavit-Hartenberg z-axis rotation matrix.
void	c_dh_translate_x (double a, double *T, int ldt)
	Build the Denavit-Hartenberg x translation matrix.
void	c_dh_translate_z (double d, double *T, int ldt)
	Build the Denavit-Hartenberg z translation matrix.
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.
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.
void	c_to_angle_axis (const double *r, int ldr, double *angle, double axis[3])
	Convert a rotation matrix to angle-axis form.
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.
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.
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.
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.
double	c_compute_modal_damping (double lambda, double alpha, double beta)
	Compute modal damping from Rayleigh coefficients.
double	c_chirp (double t, double amp, double span, double f1Hz, double f2Hz)
	Evaluate a swept-frequency chirp signal.
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.
void	c_normalize_mode_shapes (int n, double *x, int ldx)
	Normalize mode-shape columns.
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.
void	c_set_frequency_sweep_defaults (c_frequency_sweep_controls *x)
	Fill frequency-sweep controls with defaults.
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.
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.
void	c_set_iteration_controls_defaults (c_iteration_controls *x)
	Fill nonlinear iteration controls with defaults.
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.
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.
void	c_cross_product (const double x[3], const double y[3], double z[3])
	Compute the cross product of two three-vectors.
void	c_to_skew_symmetric (const double x[3], double *y, int ldy)
	Form a skew-symmetric matrix from a three-vector.
double	c_vector_angle (const double x[3], const double y[3])
	Compute the angle between two vectors.
double	c_scalar_projection (const double x[3], const double y[3])
	Compute the scalar projection of one vector onto another.
void	c_vector_projection (const double x[3], const double y[3], double z[3])
	Project one vector onto another.
double	c_vector_magnitude (int n, const double *x)
	Compute a vector magnitude.
void	c_vector_normalize (int n, double *x)
	Normalize a vector in place.
double	c_dot_product (int n, const double *x, const double *y)
	Compute a dot product.
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.
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.
void	c_set_lm_solver_options_defaults (c_lm_solver_options *x)
	Fill Levenberg-Marquardt options with defaults.
int	c_alloc_dynamic_system_measurement (int n, c_dynamic_system_measurement *x)
	Allocate one dynamic-system measurement record.
void	c_free_dynamic_system_measurement (c_dynamic_system_measurement *x)
	Release one dynamic-system measurement record.
c_dynamic_system_measurement *	c_alloc_dynamic_system_measurement_array (int n, const int *ptsper)
	Allocate an array of measurement records.
void	c_free_dynamic_system_measurement_array (int n, c_dynamic_system_measurement *x)
	Release an array of measurement records.
void	c_quaternion_from_array (const double x[4], c_quaternion *q)
	Construct a quaternion from four scalar components.
void	c_quaternion_from_matrix (const double *x, int ldx, c_quaternion *q)
	Construct a quaternion from a rotation matrix.
void	c_quaternion_from_angle_axis (double angle, const double axis[3], c_quaternion *q)
	Construct a quaternion from angle-axis data.
void	c_quaternion_normalize (c_quaternion *q)
	Normalize a quaternion in place.
void	c_quaternion_add (const c_quaternion *x, const c_quaternion *y, c_quaternion *q)
	Add two quaternions.
void	c_quaternion_subtract (const c_quaternion *x, const c_quaternion *y, c_quaternion *q)
	Subtract two quaternions.
void	c_quaternion_multiply (const c_quaternion *x, const c_quaternion *y, c_quaternion *q)
	Multiply two quaternions.
void	c_quaternion_divide (const c_quaternion *x, const c_quaternion *y, c_quaternion *q)
	Divide two quaternions.
void	c_quaternion_scale (double x, const c_quaternion *y, c_quaternion *q)
	Scale a quaternion.
void	c_quaternion_conjugate (const c_quaternion *q, c_quaternion *qc)
	Compute a quaternion conjugate.
void	c_quaternion_rotate (const c_quaternion *q, const double r[3], double rp[3])
	Rotate a vector using a quaternion.
double	c_quaternion_abs (const c_quaternion *q)
	Compute the quaternion norm.
void	c_quaternion_inverse (const c_quaternion *q, c_quaternion *qinv)
	Compute a quaternion inverse.
void	c_quaternion_to_matrix (const c_quaternion *q, double *r, int ldr)
	Convert a quaternion to a rotation matrix.
void	c_quaternion_to_angle_axis (const c_quaternion *q, double *angle, double axis[3])
	Convert a quaternion to angle-axis data.
void	c_quaternion_exp (const c_quaternion *q, c_quaternion *rst)
	Compute the quaternion exponential.
void	c_quaternion_log (const c_quaternion *q, c_quaternion *rst)
	Compute the quaternion logarithm.
void	c_quaternion_pow (const c_quaternion *q, double exponent, c_quaternion *rst)
	Raise a quaternion to a real power.
double	c_quaternion_dot_product (const c_quaternion *x, const c_quaternion *y)
	Compute the quaternion dot product.
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.
void	c_plane_normal (const c_plane *pln, double nrm[3])
	Extract a plane normal.
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.
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.
void	c_plane_from_points (int n, const double *pts, int ldp, c_plane *pln)
	Fit a plane to point data.
void	c_flip_plane_normal (c_plane *pln)
	Reverse a plane normal and its equation.
void	c_line_from_2_points (const double pt1[3], const double pt2[3], c_line *ln)
	Construct a line through two points.
void	c_line_from_2_planes (const c_plane *p1, const c_plane *p2, c_line *ln)
	Construct the intersection line of two planes.
void	c_line_from_points (int n, const double *pts, int ldp, c_line *ln)
	Fit a line to point data.
void	c_evaluate_line_position (const c_line *ln, double t, double x[3])
	Evaluate a point on a line.
bool	c_is_parallel_vectors (int n, const double *x, const double *y, double tol)
	Test whether two vectors are parallel within a tolerance.
bool	c_is_parallel_lines (const c_line *x, const c_line *y, double tol)
	Test whether two lines are parallel.
bool	c_is_parallel_planes (const c_plane *x, const c_plane *y, double tol)
	Test whether two planes are parallel.
bool	c_is_point_on_plane (const double pt[3], const c_plane *pln, double tol)
	Test whether a point lies on a plane.
bool	c_is_point_on_line (const double pt[3], const c_line *ln, double tol)
	Test whether a point lies on a 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.
double	c_point_to_line_distance (const double pt[3], const c_line *ln)
	Compute the distance from a point to a line.
double	c_point_to_plane_distance (const double pt[3], const c_plane *pln)
	Compute the distance from a point to a plane.
void	c_vector_plane_projection (const double x[3], const c_plane *pln, double px[3])
	Project a vector onto a plane.
void	c_point_plane_projection (const double pt[3], const c_plane *pln, double ppt[3])
	Project a point onto a plane.
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.
void	c_plucker_line_from_line (const c_line *src, c_plucker_line *ln)
	Convert a line to Pluecker coordinates.
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.
void	c_plucker_line_from_array (const double x[6], c_plucker_line *ln)
	Construct a Pluecker line from six coordinates.
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.
void	c_plucker_line_to_array (const c_plucker_line *ln, double x[6])
	Convert a Pluecker line to six coordinates.
void	c_line_common_normal (const c_line *ln1, const c_line *ln2, c_line *ln)
	Compute the common normal of two lines.
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.
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.
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.
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 samples with a plane.
int	c_alloc_dh_table (int n, c_dh_table *tbl)
	Allocate a Denavit-Hartenberg table.
void	c_free_dh_table (c_dh_table *tbl)
	Release a Denavit-Hartenberg table.
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.
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.
void	c_build_dh_table (int n, const c_coordinate_system *csys, c_dh_table *tbl)
	Build Denavit-Hartenberg parameters from coordinate systems.
int	c_alloc_serial_linkage (int n, c_serial_linkage *lnk)
	Allocate a serial linkage.
void	c_free_serial_linkage (c_serial_linkage *lnk)
	Release a 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.
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.
void	c_serial_linkage_jacobian (int n, const c_serial_linkage *lnk, const double *q, double *jac, int ldj)
	Evaluate the serial-link Jacobian.
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.
int	c_alloc_mechanism_link (int nframes, c_mechanism_link *lnk)
	Allocate a multi-frame mechanism link.
void	c_free_mechanism_link (c_mechanism_link *lnk)
	Release a multi-frame mechanism link.
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	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.
void	c_free_mechanism (c_mechanism obj)
	Release a mechanism handle.
int	c_mechanism_link_count (c_mechanism obj)
	Return the number of links in a mechanism.
int	c_mechanism_joint_count (c_mechanism obj)
	Return the number of joints in a mechanism.
int	c_mechanism_variable_count (c_mechanism obj)
	Return the number of mechanism variables.
int	c_mechanism_loop_count (c_mechanism obj)
	Return the number of independent loops.
int	c_mechanism_constraint_count (c_mechanism obj)
	Return the number of constraint equations.
int	c_mechanism_degrees_of_freedom (c_mechanism obj)
	Return mechanism degrees of freedom.
int	c_mechanism_actuated_variable_count (c_mechanism obj)
	Return the number of actuated variables.
int	c_mechanism_space_dimension (c_mechanism obj)
	Return the mechanism spatial dimension.
int	c_mechanism_link_frame_count (c_mechanism obj, int i)
	Return the frame count for a link.
void	c_mechanism_link_frame (c_mechanism obj, int i, int k, double *T, int ldt)
	Return a link-frame transform.
void	c_mechanism_get_configuration (c_mechanism obj, int n, double *q)
	Get the current mechanism configuration.
void	c_mechanism_set_configuration (c_mechanism obj, int n, const double *q)
	Set the mechanism configuration.
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.
void	c_mechanism_end_effector_transform (c_mechanism obj, int n, const double *q, double *T, int ldt)
	Evaluate the end-effector transform.
void	c_mechanism_constraints (c_mechanism obj, int n, const double *q, int nc, double *f)
	Evaluate mechanism constraint equations.
void	c_mechanism_constraint_jacobian (c_mechanism obj, int n, const double *q, double *jac, int ldj)
	Evaluate the mechanism constraint Jacobian.
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.
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.
void	c_mechanism_jacobian (c_mechanism obj, int na, const double *qa, double *jac, int ldj)
	Evaluate a mechanism Jacobian.
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.
void	c_default_variational_integrator_settings (c_variational_integrator_settings *settings)
	Fill variational-integrator settings with library defaults.
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_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_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.
void	c_free_linkage_dynamic_model (c_linkage_dynamic_model obj)
	Release a linkage dynamic-model handle.
int	c_linkage_dynamic_body_count (c_linkage_dynamic_model obj)
	Return the number of moving rigid bodies in a dynamic model.
int	c_linkage_dynamic_joint_count (c_linkage_dynamic_model obj)
	Return the number of joints represented by a dynamic model.
int	c_linkage_dynamic_constraint_count (c_linkage_dynamic_model obj)
	Return the linkage constraint count before any prescribed-motion constraint is added.
void	c_linkage_dynamic_add_linear_spring (c_linkage_dynamic_model obj, const c_linear_spring *element)
	Add a tension/compression linear spring.
void	c_linkage_dynamic_add_linear_damper (c_linkage_dynamic_model obj, const c_linear_damper *element)
	Add an axis-only linear viscous damper.
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.
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.
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)
	Query all axial elements at one state.
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.
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.
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.
int	c_alloc_polynomial (int order, c_polynomial *p)
	Allocate a polynomial.
void	c_free_polynomial (c_polynomial *p)
	Release a polynomial.
int	c_alloc_transfer_function (int numer_order, int denom_order, c_transfer_function *tf)
	Allocate a transfer function.
void	c_free_transfer_function (c_transfer_function *tf)
	Release a transfer function.
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.
void	c_free_state_space_model (c_state_space_model *mdl)
	Release a state-space model.
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.
void	c_transfer_function_poles (const c_transfer_function *tf, int n, double complex *p)
	Compute transfer-function poles.
void	c_transfer_function_zeros (const c_transfer_function *tf, int n, double complex *z)
	Compute transfer-function zeros.
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.
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.
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.
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.
void	c_transfer_function_multiply (const c_transfer_function *tf1, const c_transfer_function *tf2, c_transfer_function *tf)
	Multiply two transfer functions.
void	c_scale_transfer_function (double x, const c_transfer_function *tf1, c_transfer_function *tf)
	Scale a transfer function.
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.
void	c_state_space_poles (const c_state_space_model *mdl, int n, double complex *p)
	Compute state-space poles.
void	c_state_space_zeros (const c_state_space_model *mdl, int n, double complex *z, int *nz)
	Compute state-space zeros.
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.
double	c_beam_element_2d_length (const c_beam_element_2d *elem)
	Compute the length of a 2D beam element.
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.
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.
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.
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.
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.
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.
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.
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.
double	c_beam_element_3d_length (const c_beam_element_3d *elem)
	Compute the length of a 3D beam element.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
double	c_truss_element_2d_length (const c_truss_element_2d *elem)
	Compute the length of a 2D truss element.
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.
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.
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.
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.
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.
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.
double	c_truss_element_3d_length (const c_truss_element_3d *elem)
	Compute the length of a 3D truss element.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 elements.
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 elements.
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.
void	c_free_structural_integrator (c_structural_integrator obj)
	Release a structural integrator handle.
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.
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.

Detailed Description

Public C interface to the DYNAMICS library.

Matrices use column-major storage to match the Fortran implementation. A matrix with m rows and n columns has leading dimension ld and stores element (i, j) at j * ld + i, using zero-based C indices. Link, joint, and frame indices passed to the mechanism API are one-based. Objects returned by an allocation or creation routine remain owned by the caller and must be released with the corresponding c_free_* routine. Unless documented otherwise, pointer arguments must refer to storage large enough for the dimensions supplied to the routine.

Argument errors detected by this interface (for example, an undersized leading dimension or a NULL callback) do not terminate the process. The routine records the error, invokes any handler registered with c_set_error_handler, and returns without computing a result; outputs are then unspecified. Query the error with c_get_last_error. Errors detected deeper inside the Fortran library still terminate the process.

Every callback receives the user_data pointer supplied to the routine that invoked it, allowing callers to pass state without globals.

Typedef Documentation

c_error_handler

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

Error handler callback.

Parameters

code	Error code (one of the DYN_*_ERROR constants).
message	Null-terminated description, valid only during the call.
user_data	Opaque pointer supplied to c_set_error_handler.

c_vecfcn

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

Nonlinear vector function callback.

Parameters

nvar	Number of variables.
neqn	Number of equations.
x	Input variables.
f	Output residual vector.
user_data	Opaque caller data.

c_modal_excite

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

Modal force callback used by frequency-response routines.

Parameters

n	Modal count.
freq	Frequency.
f	Output modal force.
user_data	Opaque caller data.

c_harmonic_ode

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

Harmonic ordinary-differential-equation callback.

Parameters

n	State dimension.
freq	Excitation frequency.
t	Time.
x	State vector.
dxdt	Output state derivative.
user_data	Opaque caller data.

c_window_function

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

Window function callback used by SISO frequency analysis.

Parameters

n	Window length.
bin	Zero-based sample index.
user_data	Opaque caller data.

Returns

Window coefficient.

c_constraint_equations

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)

Constraint callback used by least-squares system identification.

Parameters

n	Data-set index or count.
neqn	Equation count.
nparam	Parameter count.
xg	General input values.
fg	General constraint values.
xc	Constraint inputs.
p	Model parameters.
fc	Output constraint residuals.
user_data	Opaque caller data.

c_ode_fit

typedef 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.

Parameters

n	State dimension.
nparam	Parameter count.
mdl	Model parameters.
t	Time.
x	State vector.
F	Input or forcing value.
dxdt	Output state derivative.
user_data	Opaque caller data.

c_ss_excitation

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

State-space input callback used by c_lti_solve.

Parameters

n	Input count.
t	Time.
u	Output input vector.
user_data	Opaque caller data.

c_ode_equations

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

Ordinary-differential-equation callback.

Parameters

n	State dimension.
t	Independent variable (time).
x	State vector.
dxdt	Output state derivative.
user_data	Opaque caller data.

c_poincare_coordinates

typedef void(* c_poincare_coordinates) (int n, double t, const double *x, double coordinates[3], void *user_data)

Poincare section coordinate callback.

Maps a sampled ODE state onto the coordinates intersected with the section plane.

Parameters

n	State dimension.
t	Time at which the state was sampled.
x	State vector.
coordinates	Output 3-element [x, y, z] section coordinates.
user_data	Opaque caller data.

c_variational_state

typedef struct c_variational_state c_variational_state

c_variational_force

typedef void(* c_variational_force) (const c_variational_state *state, double *force, double *torque, void *user_data)

External force and torque callback for variational integration.

Parameters

state	Current maximal-coordinate state. The pointed-to state and its arrays are read-only and valid only for the duration of the callback.
force	Output world-frame force array with shape 3-by-body_count in column-major storage.
torque	Output body-frame torque array with shape 3-by-body_count in column-major storage.
user_data	Opaque caller data supplied to the solve routine.

c_variational_constraint

typedef void(* c_variational_constraint) (const c_variational_state *state, int nconstraint, double *value, void *user_data)

Holonomic constraint callback for variational integration.

Parameters

state	Trial maximal-coordinate state at which the constraints are evaluated. The pointed-to data are valid only during the callback.
nconstraint	Number of scalar constraint equations.
value	Output array of nconstraint residual values.
user_data	Opaque caller data supplied to the solve routine.

c_variational_constraint_jacobian

typedef void(* c_variational_constraint_jacobian) (const c_variational_state *state, int nconstraint, double *jacobian, int ldj, void *user_data)

Reduced constraint-Jacobian callback.

Parameters

state	Current maximal-coordinate state at which the Jacobian is evaluated.
nconstraint	Number of Jacobian rows and scalar constraints.
jacobian	Output nconstraint-by-(6*body_count) matrix in column-major storage. Columns for each body are ordered as three translations followed by three local quaternion-tangent rotations.
ldj	Leading dimension of jacobian; equal to nconstraint.
user_data	Opaque caller data supplied to the solve routine.

c_linkage_prescribed_motion

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

Prescribed planar-link angular motion callback.

Parameters

t	Simulation time.
user_data	Opaque caller data supplied to c_linkage_dynamic_solve.

Returns

Prescribed absolute world-z angle in radians.

c_mechanism

typedef void* c_mechanism

Opaque handle to a closed-loop mechanism.

Create handles with c_create_parallel_linkage or c_create_planar_linkage, and release them with c_free_mechanism.

c_linkage_dynamic_model

typedef void* c_linkage_dynamic_model

Opaque linkage dynamic-model handle.

Create with c_create_serial_linkage_dynamic_model or c_create_linkage_dynamic_model and release with c_free_linkage_dynamic_model.

c_structural_integrator

typedef void* c_structural_integrator

Opaque linear structural time-integrator handle.

Create with c_create_dense_generalized_alpha_integrator and release with c_free_structural_integrator.