Chetaev's principle and the compatibility of the basic principles of dynamics

For material systems with nonlinear constraints, Chetaev (1962) has proposed an axiomatic definition of the concept of possible displacement. He showed that in this definition, two basic principles of dynamics, the d'Alambert-Lagrange principle and the principle of least constraint, are compatible, and has proposed an interesting version of the latter principle. In the present paper, it is shown that the extension of the possible displacement concept in the form accepted in analytical mechanics for holonomic and linear nonholonomic systems, to include nonlinear constraints leads in a natural fashion to Chetaev's definition. Generalizations of Chetaev's principle and of the principle of least constraints are proposed.