On the variational principles of mechanics

Variational principles, generalizing the classical d'Alembert-Lagrange, Holder, and Hamilton-Ostrogradskii principles, are established. After the addition of anisotropic dissipative forces and taking the limit, when the coefficient of viscous friction tends to infinity, these variational principles transform into the classical principles, which describe the motion of systems with constraints. New variational relations are established for searching for the periodic trajectories of the reversible equations of dynamics. (C) 2010 Elsevier Ltd. All rights reserved.