Cetaev condition for nonlinear nonholonomic systems and homogeneous constraints

Abstract

We first present a way to formulate the equations of motion for a nonholonomic system with nonlinear constraints with respect to the velocities. The formulation is based on the Cetaev condition which aims to extend the practical method of virtual displacements from the holonomic case to the nonlinear nonholonomic one. The condition may appear in a certain sense artificial and motivated only to coherently generalize that concerning the holonomic case. In the second part we show that for a specific category of nonholonomic constraints (homogeneous functions with respect to the generalized velocities) the Cetaev condition reveals the same physical meaning that emerges in systems with holonomic constraints. In particular the aspect of the mechanical energy associable to the system is analysed.