Integral variational principles in Poincaré and Chetayev variables

A holonomic mechanical system with k degrees of freedom is considered, its state being characterized by n k defining coordinates, p < k Poincaré parameters 1] and k - p Chetayev parameters 2]. In these variables, generalized Routh equations are introduced and expressions are given for the integral variational principles of Hamilton-Ostrogradskii and Hamilton (the third form), as well as Hölder's principle and the Lagrange and Jacobi versions of the principle of least action.