Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8417Research ArticleSolving Differential Equations of Motion for Constrained Mechanical SystemsMukharlyamovR GDepartment of Theoretical Mechanicsrobgar@mail.ruBeshawA WDepartment of Mathematicsassayewalelgn@gmail.comPeoples’ Friendship University of RussiaBahr Dar University150320133819108092016Copyright © 2013,2013This paper presents an investigation of modeling and solving system of differential equations in the study of mechanical systems with holonomic constraints. A method is developed for constracting equation of motion for mechanical system with constraints. A technique is developed how to approximate the solution of the problem that is obtained from modeling of kinematic constraint equation which is stable. A perturbation analysis shows that velocity stabilization is the most efficient projection with regard to improvement of the numerical integration. How frequently the numerical solution of the ordinary differential equation should be stabilized is discussed. A procedure is indicated to get approximate solution when the systems of differential equations can’t be solved analytically. A new approach is applied for constructing and stabilyzing Runge-Kutta numerical methods. The Runge-Kutta numerical methods are reformulated in a new approach. Not only the technique of formulation but also the test developed for its stability is new.Finally an example is presented not only to demonstrate how the stability of the solution depends on the variation of the factor but also how to find an approximate solution of the problem using numerical integration.numerical integrationkinematic constraintstable solutionTaylor expansionrow decompositionдифференциальные уравнениячисленное интегрированиекинематические ограничениястабилизацияряд Тейлора[Arabyan A., Wu F. An Improved Formulation for Constrained Mechanical Systems // Kluwer Academic Pub. — 1998. — Pp. 49–69.][Muharlyamov R. Equations of Motion of Mechanical Systems. — PFUR, 2001. — (in russian).][Gonze D. Numerical Methods to Solve Ordinary Differential Equations // P.J. Brief Bioinform. — 2009. — Pp. 53–64.][Lakoba T. Runge-Kutta Methods. — University of Vermont, 2006. — Pp. 15–20.]