Literature survey of contact dynamics modelling
d C d P n ¼
d C
d t
d t
d P n
¼
d C
d t
1
F n
ð18Þ
Eliminating the velocity time derivative by using the impulse–momentum relations,Eq.(15), allows to express the derivative of C as a function of the normal and tangential unit vectors, i.e.,
d C d P n Án¼
d C n
d P n
ðn;l tÞ;
d C
d P n
Át¼
d C t
d P n
ðn;l tÞð19Þ
where we indicated the corresponding functional dependence.Integrating the equation for the normal component C n and setting the result to zero yields an integral equation for the impulse P m. The di?erential equation for the tangential component can be integrated to solve for the tan-gential impulse de?ned in Eq.(17).
2.4.Multi-body/multi-contact impact
One disadvantage of the discrete contact modeling is that it is not easily extendible to impacts involving multiple bodies and multiple contact points.In the application of interest to us––con-strained robotics operations––simultaneous collision of several bodies is not likely to occur.It is the second situation,where contact occurs between two bodies with complex geometries at multiple points,that poses di?culties for the discrete approach.
Hurmuzlu and Marghitu[22]present a generalization of the integral–di?erential method de-scribed in Section2.3.2to a multi-body system.The equations of motion are written as MðqÞ