The principles of Lagrange–d’Alembert and Hamilton applied to a rigid bar subject to nonholonomic constraints

It is well known that the Lagrange–d’Alembert and Hamilton principles, which are widely used to derive the laws of motion for nonholonomic systems, are not equivalent and that, in some cases, the equations of motion derived from them differ. The aim of this paper is to illustrate these differences by comparing the solutions of the dynamic equations derived from these principles in a simple nonholonomic system.