Connection of first integrals with particular solutions of the nonsimultaneous variational equations for nonholonomic systems

In this paper, the nonsimultaneous variational equations of the nonholonomic mechanical systems are presented, and their solutions are studied. It is proven that, under some conditions, a particular solution of the nonsimultaneous variational equations can be obtained by using a first integral. At the end of the paper, an example is given to illustrate the applications of the results.