euler_implicit.c File Reference

This file implements the functions of the Euler Implicit integrator in C. Warning : not working yet. More...

#include "integrator.h"
#include "nrfct.h"
#include "mbs_message.h"
#include "mbs_1D_array.h"
#include "mbs_dirdyn_struct.h"
#include "mbs_euler_implicit.h"

Functions
int	euler_implicit (double y[], double dydx[], int n, double *x, double h, double yout[], int(*derivs)(double, double[], double[], MbsData *, MbsDirdyn *), MbsData *s, MbsDirdyn *mbs_dd)
	Euler Implicit integrator implementation. More...

Detailed Description

This file implements the functions of the Euler Implicit integrator in C. Warning : not working yet.

Creation date: April 2018

Author

Sebastien Timmermans

@source Arnold M. et al, Linearly implicit time integration methods in real-time applications: DAEs and stiff ODEs Multibody System Dynamics, 2007, 17:99-117

(c) Universite catholique de Louvain

Function Documentation

euler_implicit()

int euler_implicit	(	double	y[],
		double	dydx[],
		int	n,
		double *	x,
		double	h,
		double	yout[],
		int(*)(double, double[], double[], MbsData *, MbsDirdyn *)	derivs,
		MbsData *	s,
		MbsDirdyn *	mbs_dd
	)

Euler Implicit integrator implementation.

@source (adapted from) Arnold M. et al, Linearly implicit time integration methods in real-time applications: DAEs and stiff ODEs Multibody System Dynamics, 2007, 17:99–117

Parameters

y	state vector of variable
dydx	derivative of y by x
n	number of variables
x	current time value, at which the function needs to be computed
h	time step
yout	solution of the incremented variables
derivs	the function computing f'
s	the MbsData structure of the model on which dirdyn analysis is computed.
mbs_dd	the MbsDirdyn structure related to the integration.

Returns

error_code Return a negative number if something went wrong, 0 otherwise

calls an external function

A = (- h* Jv - h*h * Jp )

A = ( I - * Jv - h * h * Jp)

add 1/h in diagonal terms (identity matrix)

Compute the product : Jp * Xv

B = qdd + h * Jp * Xv

delta p = Xv + h * delta v

with delta v = B

Xv (n+1) with delta v = B

Xp (n+1)