Analysis of accelerating and braking stability using constrained bifurcation and continuation methods

Abstract

This paper proposes a method of analysing vehicle stability during acceleration and braking using constrained bifurcation and continuation methods. To apply the bifurcation analysis method originally developed to analyse the properties of dynamic systems in equilibrium, the vehicle during acceleration and braking is considered to be in an equivalent equilibrium state by assuming a virtual external force that is equal to an inertial force due to acceleration and braking is applied to the vehicle. Conventional bifurcation and continuation methods are modified to take into account constraints on state variables. The stability regions around the stable equilibrium points are also obtained to provide better understanding of the global behaviour of the vehicles. The results show the potential of the proposed method in analysing the stability of vehicles during acceleration and braking.