An Integrated Runge-Kutta and Polynomial Root Finding Method for Reliable Event-Driven Multibody Simulation

Abstract Numerical integration of dynamical equations of mechanical systems with impacts still poses many open problems. On the one hand there exist powerful integration codes with embedded root Þnding capabilities. However, for these codes, the issues of (1) efÞciency, (2) reliability and (3) stability of time progression through events still are not solved satisfactorily. In this paper, we present the implementation of a special approach for solving impact problems, in which we combine a Runge-Kutta method of order 4/5 with the Dormand coefÞcients for continuous extension dense output and a polynomial root detection algorithm. The method has been intensively tested for mechanical systems and displays robust behavior for non-stiff systems