Modeling for dynamics of rigid-body systems with friction by linear complementary problem (LCP)

The purpose of this paper is to study the modeling method for nonholonomic systems with friction by linear complementary problem (LCP). Firstly, the dynamic equation with multipliers for the nonholonomic system with friction is given. Secondly, a standard linear complementary model is established, which describes the normal and tangential characteristics for a nonholonomic system. Thirdly, by using LCP theory, a general criterion is obtained, which can identify the singularity induced by nonideal geometrical constraints in a nonholonomic system. By a typical example of a nonholonomic system with friction, it is revealed how the problem solving for the constraint reaction forces can be transformed into the standard linear complementary problem. The research work may provide reliable theoretical basis for the dynamical simulation of a nonholonomic system with non-smooth factors.