Stability analysis of vehicles on circular motions using multibody dynamics

This paper reports a method for the stability analysis of the steady curving of vehicles based on equations of motion that are obtained using multibody dynamics. The use of multibody dynamics techniques allows the systematic accurate analysis of vehicle dynamics in complex scenarios. However, stability analyses of vehicles are much more complicated than the use of conventional vehicle dynamics methods. The use of global coordinates and rotational parameters for the bodies involved implies the description of steady motions of the vehicle as periodic orbits rather than equilibrium points in the coordinate space. As a result, stability analyses must rely on Floquet's theory instead of simple eigenvalue analyses of linearized equations. In practice, applying Floquet's theory to large multibody systems involves very high computational costs. This paper reports an alternative stability analysis method based on two coordinate projections and a special eigenvalue analysis of differential algebraic equations. With this method, steady circular motions can be described in terms of equilibrium points rather than periodic motions. Stability analyses are thus made much more simple and computationally efficient. By way of example, the method was applied to a simple wheeled mechanism. The numerical results thus obtained were consistent with those of analytical and classical theories, which testifies to the accuracy of the proposed method.