Non-linear aspects in the computation of the kinetic parameters for multi-body systems with friction

Abstract

Because of the friction laws, the equation for the computation of the kinetic parameters (accelerations and reaction forces) for systems with friction-affected constraints are non-linear. Consequently, the existence and uniqueness of solutions are not assured, and, in general, only numerical and iterative computation methods are applicable. With the help of influence coefficients the kinetic equations are reformulated suitably for the application of trial-and-error based procedures. These procedures extend the cases when closed-form solutions can be determined and, for the general case, show better convergence properties than pure iteration schemes. The meaning of some influence coefficients, the convergence or non-convergence of iteration schemes and the bifurcation of the solutions with increasing friction parameters are illustrated by an example.