On generalized Routh's equations and variational principles in Poincare and Chetayev variables

摘要

The generalized Routh's equations are deduced in Poincare and Chetayev variables. Expressions are presented in these variables for the D'Alembert-Lagrange. Hamilton-Ostrogragskii and Hamilton (third form) variational principles, as well as for the Holder principle and the Lagrange principle of least action.