On the analytical mechanics methods in mathematical modeling the dynamics systems with geometric constraints

A necessary condition for the most effective application of the mathematical control theory results to the modern automatic devices dynamics сonsideration is the presence of an adequate nonlinear mathematical model obtained by strict general methods. Methods for reducing the dimensions of dynamic models of systems with geometric constraints by analytical mechanics methods for non-free systems are considered due to the transition to equations in redundant coordinates free of constraint multipliers. A detailed algorithm for this procedure and its justification is given. Using the theory of critical cases, a complete solution is given to the stabilizing problem of a given configuration of systems with geometric constraints.