Variational principles for systems with unilateral constraints

Derivations and formulations are given of the variational principles of analytical mechanics for systems with unilateral ideal smooth constraints, originally established for systems with bilateral constraints. The virtual work principle, the Fourier inequality, the d’Alembert–Lagrange principle, the Gauss principle of least constraint and its modification – the Chetayev principle of maximum work, the Jourdain principle, the Hamilton–Ostrogradskii principle, the principle of least action in Lagrangian and Jacobian forms, and the Suslov–Voronets principle are described.