A methodology for simulations of multi-rigid body systems with topology changes

Abstract

This paper represents a simple and accurate method based on the impulse–momentum equation for the numerical simulation of multi-body systems with topology changes. The method takes full advantage of Lagrangian equations of the first type, which are the differential algebra equations (DAEs) of a multi-rigid body system. The basic concept is to integrate dynamic equations over a topologically changing duration that is a short period of time to obtain impulse-momentum equations. Next, the topology change event can be treated as an instantaneous progression in the numerical simulation. Additionally, constraint violation elimination was fully considered for the accuracy of the subsequent calculations after the topology changes. This method is applicable for systems with chain, tree and close-loop topologies. Two numerical test cases of chain and close-loop systems are simulated to testify the efficiency and accuracy of this methodology.