Integral principles for nonlinear nonholonomic systems

This paper discusses the equivalence of the integral principles in the forms due to the fact that Holder, Suslov and Voronets shows them to be different forms of Hamilton's principle for nonholonomic systems with Chetaev's constraints. Necessary and sufficient conditions are obtained for the stationarity of actions in the sense of Hamilton, Lagrange and Jacobi. Also, the necessary and sufficient conditions are given for the applicability of the generalized Hamilton-Jacobi method of integrating the equations of motion of a nonholonomic system. It is shown that these conditions are equivalent to the conditions mentioned for the integral principles.