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

Abstract

This nbsp article nbsp is nbsp devoted nbsp to nbsp constructing nbsp equations nbsp of nbsp motion nbsp for nbsp Holonomic nbsp systems nbsp using nbsp Lagrangian nbsp variables nbsp We nbsp introduce nbsp the nbsp form nbsp of nbsp equations nbsp which nbsp allow nbsp for detailed analyses of both linear and non linear terms of perturbed motion equations nbsp Steady nbsp motion nbsp stability nbsp of nbsp systems nbsp with nbsp redundant nbsp coordinates nbsp is nbsp only nbsp possible nbsp in nbsp critical nbsp cases nbsp e g nbsp when nbsp the nbsp characteristic nbsp equation nbsp has nbsp roots nbsp whose nbsp real nbsp parts nbsp 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 nbsp systems nbsp with nbsp geometric nbsp constraints nbsp The nbsp method nbsp is nbsp based nbsp on nbsp analytical nbsp mechanics theory of critical cases nonlinear stability theory and N N Krasovsky rsquo s nbsp procedure nbsp of nbsp solving nbsp linear quadratic nbsp problems nbsp This nbsp grants nbsp the nbsp ability nbsp to nbsp make reasonable nbsp conclusions nbsp regarding nbsp system nbsp stability nbsp and nbsp calculations nbsp and nbsp calculate coefficients of the linear stabilizing control