An LCP method for dynamics of planar-motion rigid-body with non-symmetric friction

A modeling and numerical calculation method for the dynamics of the rigid-body in planar motion with contact, impact, symmetric and non-symmetric Coulomb's dry friction was presented based on the theory of contact mechanics and the arithmetic of linear complementarity problem (LCP). The local deformations in contact bodies were taken into account although bodies were assumed to be rigid. The normal contact forces were expressed as nonlinear functions of penetration depth and its speed. The friction law adopted symmetric or non-symmetric Coulomb's dry friction model. Firstly, by using the friction saturation, the positive and negative parts of the relative acceleration of contact points, the complementarity conditions and formulations about the friction law were given in order to determine state transitions of stick-slip in numerical method. Then, based on the event-driven scheme, the problems of detecting stick-slip state transitions and solving frictional forces in stick situation were formulated and solved as a linear complementarity problem. Finally, the numerical example of a planar-motion rigid-body was given to analyze its dynamical behaviour affected by symmetric or non-symmetric Coulomb's dry friction and shown that the proposed method was effective.