About Mathematical Models of System Dynamics with Geometric Constraints in Problems of Stability and Stabilization by Incomplete State Information

摘要

This article is devoted to constructing equations of motion for Holonomic systems using Lagrangian variables. We introduce the form of equations which allow for detailed analyses of both linear and non-linear terms of perturbed motion equations. Steady motion stability of systems with redundant coordinates is only possible in critical cases; e.g. when the characteristic equation has roots whose real parts are zero. In this case, it is imperative to analyze the nonlinear terms of the characteristic equation to solve stability issues. We suggest a rigorous method of solving stability problem for systems with geometric constraints. The method is based on analytical mechanics, theory of critical cases, nonlinear stability theory, and N.N. Krasovsky’s procedure of solving linear-quadratic problems. This grants the ability to make reasonable conclusions regarding system stability and calculations and calculate coefficients of the linear stabilizing control.