To derive Lagrange equations of nonholonomic systems without using the Chetaev conditions

The present paper derives the equation of motion for a class of nonholonomic dynamical systems from the d'Alembert-Lagrange equation. In this paper, the relation dδ = δd is assumed only for those generalized coordinates whose variations are independent. For the remaining coordinates, the transpositional relations are derived by means of mathematics method, which are different from the Chetaev condition. Several examples are given.