Dynamics, Friction, and Complementarity Problems
2
D.E. Stewart
J.C. Trinkle
International Conference on Complementarity Problems, Johns Hopkins University, Baltimore, Nov. 1995
1995 JHU
http://www.cs.tamu.edu/research/robotics/Trink/Papers/iccp95StewTrink.ps
An overview is presented here of recent work and approaches to solving
dynamic problems in rigid body mechanics with friction. It begins with
the differential inclusion approach to Coulomb friction where the
normal contact force is known.  Numerical methods for these
differential inclusions commonly lead to linear and nonlinear
complementarity problems.  Then the measure differential inclusion
formulation of rigid body dynamics due to Moreau and others is
presented. A novel algorithm for time-stepping for rigid body dynamics
is given which avoids the "nonexistence" issues that arise in many
other formulations. The time-stepping algorithm requires the solution
of a nonlinear complementarity problem at each step. Results on the
convergence of the numerical solutions to solutions in the sense of
measure differential inclusions are given, and numerical results for
an implementation of the method are shown.