The principles of Gauss and Chetaev for systems with nonideal couplings

A system of material points is considered, which is constrained by couplings which are nonlinear relative to the velocities of the points, nonintegrable, independent of one another, and nonideal. The Dalembert-Lagrange principle, Gauss's principle, and Chetaev's modification of Gauss's principle, dealing with the reaction work of the couplings and the liberation of the points from the couplings, are discussed and generalized.