#include "math.h"
#include "mbs_data.h"
#include "mbs_1D_array.h"

Macros
#define	_USE_MATH_DEFINES

Functions
double *	user_Link3DForces_dq (double PxF[4], double d_PxF[4], double RxF[4][4], double d_RxF[4][4], double VxF[4], double d_VxF[4], double OMxF[4], double d_OMxF[4], double AxF[4], double d_AxF[4], double OMPxF[4], double d_OMPxF[4], MbsData *s, double tsim, int i_link3d, int i_param)
	Compute the partial derivative of a link3D forces with respect to a generalized coordinate. More...

double *	user_Link3DForces_dqd (double PxF[4], double d_PxF[4], double RxF[4][4], double d_RxF[4][4], double VxF[4], double d_VxF[4], double OMxF[4], double d_OMxF[4], double AxF[4], double d_AxF[4], double OMPxF[4], double d_OMPxF[4], MbsData *s, double tsim, int i_link3d, int i_param)
	Compute the partial derivative of a link3D forces with respect to a generalized velocity. More...

double *	user_Link3DForces_dqdd (double PxF[4], double d_PxF[4], double RxF[4][4], double d_RxF[4][4], double VxF[4], double d_VxF[4], double OMxF[4], double d_OMxF[4], double AxF[4], double d_AxF[4], double OMPxF[4], double d_OMPxF[4], MbsData *s, double tsim, int i_link3d, int i_param)
	Compute the partial derivative of a link3D forces with respect to a generalized acceleration. More...

double *	user_Link3DForces_dp (double PxF[4], double d_PxF[4], double RxF[4][4], double d_RxF[4][4], double VxF[4], double d_VxF[4], double OMxF[4], double d_OMxF[4], double AxF[4], double d_AxF[4], double OMPxF[4], double d_OMPxF[4], MbsData *s, double tsim, int i_link3d)
	Compute the partial derivative of a link3D forces with respect to a parameter. More...

Macro Definition Documentation

◆ _USE_MATH_DEFINES

#define _USE_MATH_DEFINES

Function Documentation

◆ user_Link3DForces_dp()

double* user_Link3DForces_dp	(	double	PxF[4],
		double	d_PxF[4],
		double	RxF[4][4],
		double	d_RxF[4][4],
		double	VxF[4],
		double	d_VxF[4],
		double	OMxF[4],
		double	d_OMxF[4],
		double	AxF[4],
		double	d_AxF[4],
		double	OMPxF[4],
		double	d_OMPxF[4],
		MbsData *	s,
		double	tsim,
		int	i_link3d
	)

Compute the partial derivative of a link3D forces with respect to a parameter.

Parameters

[in]	PxF	The vector "AB" (index starting at 1) with components expressed in frame [P].
[in]	d_PxF	the partial derivative of `PxF` with respect to the generalized coordinate of joint `i_joint:` $d\_PxF = \frac{\partial PxF}{\partial q_{i\_joint}}$ .
[in]	RxF	The rotation matrix (index starting at 1) such as [C] = Rxf*[P].
[in]	d_RxF	the partial derivative of matrix `RxF` with respect to the generalized coordinate of joint `i_joint:` $d\_RxF = \frac{\partial RxF}{\partial q_{i\_joint}}$ .
[in]	VxF	The differential velocity vector (index starting at 1) with components expressed in frame [P]. The velocities are computed at the coordinates of point "M" linked to parent (Md_p), then linked to children (Md_c) body. The differential velocity vector is : Md_c - Md_p.
[in]	d_VxF	the partial derivative of `VxF` with respect to the generalized coordinate of joint `i_joint:` $d\_VxF = \frac{\partial VxF}{\partial q_{i\_joint}}$ .
[in]	OMxF	The differential angular velocity vector (index starting at 1) with components expressed in frame [P]. It is the difference between the parent angular velocity and the children angular velocity.
[in]	d_OMxF	the partial derivative of `OMxF` with respect to the generalized coordinate of joint `i_joint:` $d\_OMxF = \frac{\partial OMxF}{\partial q_{i\_joint}}$ .
[in]	AxF	The differential acceleration vector (index starting at 1) with components expressed in frame [P]. The accelerations are computed at the coordinates of point "M" linked to parent (Mdd_p), then linked to children (Mdd_c) body. The differential acceleration vector is : Mdd_c - Mdd_p.
[in]	d_AxF	the partial derivative of `AxF` with respect to the generalized coordinate of joint `i_joint:` $d\_AxF = \frac{\partial AxF}{\partial q_{i\_joint}}$ .
[in]	OMPxF	The differential angular acceleration vector (index starting at 1) with components expressed in frame [P]. It is the difference between the parent angular acceleration and the children angular acceleration.
[in]	d_OMPxF	the partial derivative of `OMPxF` with respect to the generalized coordinate of joint `i_joint:` $d\_OMPxF = \frac{\partial OMPxF}{\partial q_{i\_joint}}$ .
[in,out]	s	The MbsData structure of the model on which the force is computed.
[in]	tsim	The current time of the simulation
[in]	i_link3d	The ID identifying the computed link3D force.

Returns

The partial derivative of the link3D force with respect to generalized parameter i_joint: The content of the returned vector dSWr_link3d_dp is [dF_dq; dMx_dq; ddxF_dq]:

Partial derivative of the link3d components (expressed in the inertial frame): dF_dq = $\left[\frac{\partial Fx}{\partial q_{i\_joint}} ; \frac{\partial Fy}{\partial q_{i\_joint}} ; \frac{\partial Fz}{\partial q_{i\_joint}}\right]$
Partial derivative of the pure torque components (expressed in the inertial frame): dM_dq = $\left[\frac{\partial Mx}{\partial q_{i\_joint}} ; \frac{\partial My}{\partial q_{i\_joint}} ; \frac{\partial Mz}{\partial q_{i\_joint}}\right]$
Partial derivative of the application point local coordinates vector (expressed in the body-fixed frame): ddxF_dq = $\left[\frac{\partial dxF}{\partial q_{i\_joint}} ; \frac{\partial dxF}{\partial q_{i\_joint}} ; \frac{\partial dxF}{\partial q_{i\_joint}}\right]$

In 1D, it gives:
$d\_Flink3D_{i\_link3D} = \frac{\partial Flink3D_{i\_link3D}}{\partial q_{i\_joint}}$

.

◆ user_Link3DForces_dq()

double* user_Link3DForces_dq	(	double	PxF[4],
		double	d_PxF[4],
		double	RxF[4][4],
		double	d_RxF[4][4],
		double	VxF[4],
		double	d_VxF[4],
		double	OMxF[4],
		double	d_OMxF[4],
		double	AxF[4],
		double	d_AxF[4],
		double	OMPxF[4],
		double	d_OMPxF[4],
		MbsData *	s,
		double	tsim,
		int	i_link3d,
		int	i_param
	)

Compute the partial derivative of a link3D forces with respect to a generalized coordinate.

Parameters

[in]	PxF	The vector "AB" (index starting at 1) with components expressed in frame [P].
[in]	d_PxF	the partial derivative of `PxF` with respect to the generalized coordinate of joint `i_joint:` $d\_PxF = \frac{\partial PxF}{\partial q_{i\_joint}}$ .
[in]	RxF	The rotation matrix (index starting at 1) such as [C] = Rxf*[P].
[in]	d_RxF	the partial derivative of matrix `RxF` with respect to the generalized coordinate of joint `i_joint:` $d\_RxF = \frac{\partial RxF}{\partial q_{i\_joint}}$ .
[in]	VxF	The differential velocity vector (index starting at 1) with components expressed in frame [P]. The velocities are computed at the coordinates of point "M" linked to parent (Md_p), then linked to children (Md_c) body. The differential velocity vector is : Md_c - Md_p.
[in]	d_VxF	the partial derivative of `VxF` with respect to the generalized coordinate of joint `i_joint:` $d\_VxF = \frac{\partial VxF}{\partial q_{i\_joint}}$ .
[in]	OMxF	The differential angular velocity vector (index starting at 1) with components expressed in frame [P]. It is the difference between the parent angular velocity and the children angular velocity.
[in]	d_OMxF	the partial derivative of `OMxF` with respect to the generalized coordinate of joint `i_joint:` $d\_OMxF = \frac{\partial OMxF}{\partial q_{i\_joint}}$ .
[in]	AxF	The differential acceleration vector (index starting at 1) with components expressed in frame [P]. The accelerations are computed at the coordinates of point "M" linked to parent (Mdd_p), then linked to children (Mdd_c) body. The differential acceleration vector is : Mdd_c - Mdd_p.
[in]	d_AxF	the partial derivative of `AxF` with respect to the generalized coordinate of joint `i_joint:` $d\_AxF = \frac{\partial AxF}{\partial q_{i\_joint}}$ .
[in]	OMPxF	The differential angular acceleration vector (index starting at 1) with components expressed in frame [P]. It is the difference between the parent angular acceleration and the children angular acceleration.
[in]	d_OMPxF	the partial derivative of `OMPxF` with respect to the generalized coordinate of joint `i_joint:` $d\_OMPxF = \frac{\partial OMPxF}{\partial q_{i\_joint}}$ .
[in,out]	s	The MbsData structure of the model on which the force is computed.
[in]	tsim	The current time of the simulation
[in]	i_link3d	The ID identifying the computed link3D force
[in]	i_param	The id of the parameter.

Returns

The partial derivative of the link3D force with respect to generalized coordinate i_joint: The content of the returned vector dSWr_link3d_dq is [dF_dq; dMx_dq; ddxF_dq]:

Partial derivative of the link3d components (expressed in the inertial frame): dF_dq = $\left[\frac{\partial Fx}{\partial q_{i\_joint}} ; \frac{\partial Fy}{\partial q_{i\_joint}} ; \frac{\partial Fz}{\partial q_{i\_joint}}\right]$
Partial derivative of the pure torque components (expressed in the inertial frame): dM_dq = $\left[\frac{\partial Mx}{\partial q_{i\_joint}} ; \frac{\partial My}{\partial q_{i\_joint}} ; \frac{\partial Mz}{\partial q_{i\_joint}}\right]$
Partial derivative of the application point local coordinates vector (expressed in the body-fixed frame): ddxF_dq = $\left[\frac{\partial dxF}{\partial q_{i\_joint}} ; \frac{\partial dxF}{\partial q_{i\_joint}} ; \frac{\partial dxF}{\partial q_{i\_joint}}\right]$

In 1D, it gives:
$d\_Flink3D_{i\_link3D} = \frac{\partial Flink3D_{i\_link3D}}{\partial q_{i\_joint}}$

.

◆ user_Link3DForces_dqd()

double* user_Link3DForces_dqd	(	double	PxF[4],
		double	d_PxF[4],
		double	RxF[4][4],
		double	d_RxF[4][4],
		double	VxF[4],
		double	d_VxF[4],
		double	OMxF[4],
		double	d_OMxF[4],
		double	AxF[4],
		double	d_AxF[4],
		double	OMPxF[4],
		double	d_OMPxF[4],
		MbsData *	s,
		double	tsim,
		int	i_link3d,
		int	i_param
	)

Compute the partial derivative of a link3D forces with respect to a generalized velocity.

Parameters

[in]	PxF	The vector "AB" (index starting at 1) with components expressed in frame [P].
[in]	d_PxF	the partial derivative of `PxF` with respect to the generalized coordinate of joint `i_joint:` $d\_PxF = \frac{\partial PxF}{\partial q_{i\_joint}}$ .
[in]	RxF	The rotation matrix (index starting at 1) such as [C] = Rxf*[P].
[in]	d_RxF	the partial derivative of matrix `RxF` with respect to the generalized coordinate of joint `i_joint:` $d\_RxF = \frac{\partial RxF}{\partial q_{i\_joint}}$ .
[in]	VxF	The differential velocity vector (index starting at 1) with components expressed in frame [P]. The velocities are computed at the coordinates of point "M" linked to parent (Md_p), then linked to children (Md_c) body. The differential velocity vector is : Md_c - Md_p.
[in]	d_VxF	the partial derivative of `VxF` with respect to the generalized coordinate of joint `i_joint:` $d\_VxF = \frac{\partial VxF}{\partial q_{i\_joint}}$ .
[in]	OMxF	The differential angular velocity vector (index starting at 1) with components expressed in frame [P]. It is the difference between the parent angular velocity and the children angular velocity.
[in]	d_OMxF	the partial derivative of `OMxF` with respect to the generalized coordinate of joint `i_joint:` $d\_OMxF = \frac{\partial OMxF}{\partial q_{i\_joint}}$ .
[in]	AxF	The differential acceleration vector (index starting at 1) with components expressed in frame [P]. The accelerations are computed at the coordinates of point "M" linked to parent (Mdd_p), then linked to children (Mdd_c) body. The differential acceleration vector is : Mdd_c - Mdd_p.
[in]	d_AxF	the partial derivative of `AxF` with respect to the generalized coordinate of joint `i_joint:` $d\_AxF = \frac{\partial AxF}{\partial q_{i\_joint}}$ .
[in]	OMPxF	The differential angular acceleration vector (index starting at 1) with components expressed in frame [P]. It is the difference between the parent angular acceleration and the children angular acceleration.
[in]	d_OMPxF	the partial derivative of `OMPxF` with respect to the generalized coordinate of joint `i_joint:` $d\_OMPxF = \frac{\partial OMPxF}{\partial q_{i\_joint}}$ .
[in,out]	s	The MbsData structure of the model on which the force is computed.
[in]	tsim	The current time of the simulation
[in]	i_link3d	The ID identifying the computed link3D force.
[in]	i_param	The id of the parameter.

Returns: A vector (of size 9, index starting at 0) with the content described for MbsData::mbs_dp->dSWr_link3d_dqd

The content of the returned vector dSWr_dqd is [dF_dqd; dMx_dqd; ddxF_dqd]:

Partial derivative of the force components (expressed in the inertial frame): dF_dqd = $\left[\frac{\partial Fx}{\partial \dot{q}_{i\_joint}} ; \frac{\partial Fy}{\partial \dot{q}_{i\_joint}} ; \frac{\partial Fz}{\partial \dot{q}_{i\_joint}}\right]$
Partial derivative of the pure torque components (expressed in the inertial frame): dM_dqd = $\left[\frac{\partial Mx}{\partial \dot{q}_{i\_joint}} ; \frac{\partial My}{\partial \dot{q}_{i\_joint}} ; \frac{\partial Mz}{\partial \dot{q}_{i\_joint}}\right]$
Partial derivative of the application point local coordinates vector (expressed in the body-fixed frame): ddxF_dqd = $\left[\frac{\partial dxF}{\partial \dot{q}_{i\_joint}} ; \frac{\partial dxF}{\partial \dot{q}_{i\_joint}} ; \frac{\partial dxF}{\partial \dot{q}_{i\_joint}}\right]$

◆ user_Link3DForces_dqdd()

double* user_Link3DForces_dqdd	(	double	PxF[4],
		double	d_PxF[4],
		double	RxF[4][4],
		double	d_RxF[4][4],
		double	VxF[4],
		double	d_VxF[4],
		double	OMxF[4],
		double	d_OMxF[4],
		double	AxF[4],
		double	d_AxF[4],
		double	OMPxF[4],
		double	d_OMPxF[4],
		MbsData *	s,
		double	tsim,
		int	i_link3d,
		int	i_param
	)

Compute the partial derivative of a link3D forces with respect to a generalized acceleration.

Parameters

[in]	PxF	The vector "AB" (index starting at 1) with components expressed in frame [P].
[in]	d_PxF	the partial derivative of `PxF` with respect to the generalized coordinate of joint `i_joint:` $d\_PxF = \frac{\partial PxF}{\partial q_{i\_joint}}$ .
[in]	RxF	The rotation matrix (index starting at 1) such as [C] = Rxf*[P].
[in]	d_RxF	the partial derivative of matrix `RxF` with respect to the generalized coordinate of joint `i_joint:` $d\_RxF = \frac{\partial RxF}{\partial q_{i\_joint}}$ .
[in]	VxF	The differential velocity vector (index starting at 1) with components expressed in frame [P]. The velocities are computed at the coordinates of point "M" linked to parent (Md_p), then linked to children (Md_c) body. The differential velocity vector is : Md_c - Md_p.
[in]	d_VxF	the partial derivative of `VxF` with respect to the generalized coordinate of joint `i_joint:` $d\_VxF = \frac{\partial VxF}{\partial q_{i\_joint}}$ .
[in]	OMxF	The differential angular velocity vector (index starting at 1) with components expressed in frame [P]. It is the difference between the parent angular velocity and the children angular velocity.
[in]	d_OMxF	the partial derivative of `OMxF` with respect to the generalized coordinate of joint `i_joint:` $d\_OMxF = \frac{\partial OMxF}{\partial q_{i\_joint}}$ .
[in]	AxF	The differential acceleration vector (index starting at 1) with components expressed in frame [P]. The accelerations are computed at the coordinates of point "M" linked to parent (Mdd_p), then linked to children (Mdd_c) body. The differential acceleration vector is : Mdd_c - Mdd_p.
[in]	d_AxF	the partial derivative of `AxF` with respect to the generalized coordinate of joint `i_joint:` $d\_AxF = \frac{\partial AxF}{\partial q_{i\_joint}}$ .
[in]	OMPxF	The differential angular acceleration vector (index starting at 1) with components expressed in frame [P]. It is the difference between the parent angular acceleration and the children angular acceleration.
[in]	d_OMPxF	the partial derivative of `OMPxF` with respect to the generalized coordinate of joint `i_joint:` $d\_OMPxF = \frac{\partial OMPxF}{\partial q_{i\_joint}}$ .
[in,out]	s	The MbsData structure of the model on which the force is computed.
[in]	tsim	The current time of the simulation
[in]	i_link3d	The ID identifying the computed link3D force.
[in]	i_param	The id of the parameter.

Returns

The partial derivative of the link3D force with respect to generalized acceleration i_joint: The content of the returned vector dSWr_link3d_dqdd is [dF_dq; dMx_dq; ddxF_dq]:

Partial derivative of the link3d components (expressed in the inertial frame): dF_dq = $\left[\frac{\partial Fx}{\partial q_{i\_joint}} ; \frac{\partial Fy}{\partial q_{i\_joint}} ; \frac{\partial Fz}{\partial q_{i\_joint}}\right]$
Partial derivative of the pure torque components (expressed in the inertial frame): dM_dq = $\left[\frac{\partial Mx}{\partial q_{i\_joint}} ; \frac{\partial My}{\partial q_{i\_joint}} ; \frac{\partial Mz}{\partial q_{i\_joint}}\right]$
Partial derivative of the application point local coordinates vector (expressed in the body-fixed frame): ddxF_dq = $\left[\frac{\partial dxF}{\partial q_{i\_joint}} ; \frac{\partial dxF}{\partial q_{i\_joint}} ; \frac{\partial dxF}{\partial q_{i\_joint}}\right]$

In 1D, it gives:
$d\_Flink3D_{i\_link3D} = \frac{\partial Flink3D_{i\_link3D}}{\partial q_{i\_joint}}$

.

Macros

Functions

Macro Definition Documentation

◆ _USE_MATH_DEFINES

Function Documentation

◆ user_Link3DForces_dp()

◆ user_Link3DForces_dq()

◆ user_Link3DForces_dqd()

◆ user_Link3DForces_dqdd()