Extensions of Appell's and Tzènoff's equations to general nonholonomic systems

In this paper we present a new variational principle, from which Gauss principle can be derived as a corollary. By using the new principle, Appell's and Tzènoff's equations are extended to nonholonomic systems of any order. As an example, a second order nonholonomic system is given to illustrate the application of the equations obtained.