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.

A virtual rider for two-wheeled vehicles

“…These vibration modes have been deeply investigated in the past years, see e.g. [15]- [22]. The root-locus of the vehicle used is presented herein to highlight how its dynamics change with speed, lateral and longitudinal acceleration, and to show that the behavior of the numerical model is consistent with the other advanced models reported in the literature.…”

State-of-the-art and challenges of railway and road vehicle dynamics with multibody dynamics approaches

“…For the analysis of the stability during braking conditions, the same kind of modelling, including the linearization, was used in [135]. The concept of practical stability, which takes Fig.…”