Practical stability analysis for transient system dynamics

Abstract

The stability of multi-body systems in transient conditions, such as vehicles under braking, is considered. Stability in this case is not univocal, because according to the widely used classical definitions of Lyapunov and Malkin, nearly all motions taking place over a finite time are stable. Here, the use of the concept of practical stability is proposed, which is concerned with a limited growth of perturbations expected to be present in a real system. A viable calculation procedure for applying this concept to multi-body systems is proposed, in which the equations of motion and their linearizations are generated and analysed in a symbolic program, AutoSim. Applications are made to the acceleration of a non-linear Jeffcott rotor through its critical speed and the braking of a motorcycle. The rotor remains stable, provided that the acceleration is sufficiently large and the mass eccentricity sufficiently small. For the motorcycle, braking mainly enhances the wobble mode, whereas locking of the rear wheel may lead to a fall.