Теоретическая механика UDC 531.3 Stabilization of Redundantly Constrained Dynamic System R. G. Mukharlyamov, Chernet Tuge Deressa Department of Theoretical Physics and Mechanics Peoples’ Friendship University of Russia 6, Miklukho-Maklaya str., Moscow, Russia, 117198 This article addresses the issue of constraint stabilization in a dynamic system. <...> The well known Lagrange’s equation of motion of second order is used for modelling the dynamics of a mechanical systems considered in this paper. <...> It is known that Baumgarte’s method of constraint stabilization does not avoid the problem of singularity of mass matrices that may result from redundancy of constraints and as a result it fails to run simulations near and at singularity points. <...> A generalized Baumgarte’s method of constraint stabilization is developed and the stability of the developed method is ascertained by Lyapunov’s direct method. <...> The developed method avoids using the same correction parameters for all constraints under discussion. <...> The usual Baumgarte’s method, which uses the same correction parameters, becomes a particular case of the one developed in this article. <...> Moreover, a modified Lagrange’s equation is constructed in a way that explains all the details of its derivation. <...> The modified Lagrange’s equation improves Lagrange’s equation of motion in such a way that, it addresses the issue of redundant constraints and singular mass matrices. <...> As it is the case in Baumgarte’s method, the usual Lagrange’s equation is a particular case of the improved method developed in this paper. <...> Besides, a numerical example is provided in order to demonstrate the effectiveness of the methods developed. <...> Finally, the carried out simulations show asymptotic stability of the trajectories and run without problem at singularity points. <...> Key words and phrases: stability, generalized Baumgarte’s method, modified Lagrange’s equation, singular mass matrices, redundant constraints, Lyapunov’s direct method. 1. <...> Introduction One of the commonly used method of modeling Dynamics of Constrained mechanical systems is Lagrange’s equation of motion [1–3]. <...> This method of constructing motion equations of a mechanical system results in a set of Index 3 Differential Algebraic Equations (DAE). <...> These set of DAE of motion does not use <...>