Complementarity Formulations and Existence of Solutions of Dynamic Multi-Rigid-Body Contact Problems with Coulomb Friction
2
J.S. Pang
J.C. Trinkle
Mathematical Programming, to appear
1996 MPS
http://www.cs.tamu.edu/faculty/trink/Papers/PT_math_prog.ps.Z
In this paper, we study the problem of predicting the acceleration of
a set of rigid, 3-dimensional bodies in contact with Coulomb
friction. The nonlinearity of Coulomb's law leads to a nonlinear
complementarity formulation of the system model. This model is used in
conjunction with the theory of quasi-variational inequalities to prove
for the first time that multi-rigid-body systems with all contacts
rolling always has a solution under a feasibility-type condition. The
analysis of the more general problem with sliding and rolling contacts
presents difficulties that motivate our consideration of a relaxed
friction law. The corresponding complementarity formulations of the
multi-rigid-body contact problem are derived and existence of
solutions of these models is established.

Dedication: It gives us great pleasure to dedicate this paper to
Professor Richard W. Cottle for his sixtieth birthday on 29 June
1994. Professor Cottle is the founder of the linear complementarity
problem. This paper is motivated by an engineering application; like
many such applications, complementarity plays a central role in the
problem formulation, analysis, and solution. We are indebted to
Professor Cottle for the fundamental contributions he has made in this
field, for his constant encouragement, advice, and fruitful
collaboration over many years. Without his help and guidance, this
work would not have been possible.