Computer-Aided Integration of Motions of the Discontinuous Mechanical System

Abstract

Consideration was given to computer-aided modeling of the dynamics of multiple-link manipulators and other mechanical systems. Various perturbing factors that can affect this process were examined. Conditions for correct modeling that provides motions close to those of the physical system were established. Motion of the mechanical system is often described by differential equations whose computer-aided integration is usually defined as difference schemes that occur, for example, if finiteness of the integration step is taken into account. For the differential equations with smooth right-hand sides, sufficiently efficient methods of constructing an adequate scheme of integration were developed. The present paper focused on the mechanical systems where the generalized forces may be discontinuous. Construction of an adequate integration scheme for them is a challenge. Established were the conditions for motions of the difference scheme to converge to those of the system of discontinuous differential equations of the mechanical system.