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)8268Research ArticleOn Solving Differential Kinematic Equations for Constrained Mechanical SystemsBeshawA WDepartment of Mathematicsassayewalelgn@gmail.comBahr Dar University150220152192708092016Copyright © 2015,2015This paper proposes a method for constructing the kinematic equations of the mechanical system, which imposed geometric constraints. The method is based on the consideration of kinematic constraints as particular integrals of the required system of diﬀerential equations. Runge-Kutta method is used for the numerical solution of nonlinear diﬀerential equations. The developed methods allow us to estimate the range of variation of the parameters during the numerical solution which determine conditions for stabilization with respect to constraint equations. The numerical results illustrate the dependence on the stabilization of the numerical solution is not only due to the asymptotic stability with respect to the constraint equations, but also through the use of diﬀerence schemes of higher order accuracy. To estimate the accuracy of performance of the constraint equations additional parameters are introduced that describe the change in purpose-built perturbation equations. It is shown that unstable solution, with respect to constraint equations, obtained by the Euler method can be stable by using Runge-Kutta method.kinematic constraintspseudo-inverseapproximate solutionstabilityEuler’s methodRunge-Kutta methodsкинематические ограниченияприближенное решениепсевдообратныйустойчивостьметод Эйлераметоды Рунге-КуттыМухарлямов Р.Г., Абрамов Н.В., Киргираев Ж.К. Уравнение динамики системы с программными связями. - Юргу, 2013.Mukharlyamov R.G. On the Construction of Differential Equations of Motion of Constrained Mechanical Systems, Differential Equations // Differential Equations. - 2003. - Vol. 39, No 3. - Pp. 343-353.Мухарлямов Р.Г. Уравнение движения механических систем. - РУДН, 2001.Edwadia F.E. Recent Advances in Multi-body Dynamics and Nonlinear Control // ABCM. - 2006. - Vol. 28, No 3. - Pp. 311-315.Mukharlyamov R.G. On the Equations of Kinematics and Dynamics of Constrained Mechanical Systems // Multibody System Dynamics. - 2001. - No 6. - Pp. 17-28.Мухарлямов Р.Г., Бешау А.В. Решение дифференциальных уравнений движения для механических систем со связями // Вестник рУДН. Серия «Математика. Информатика. Физика». - 2013. - № 3. - С. 81-91.Fenton J.D. Numerical Methods // Karlsplatz. - 2010. - No 3. - Pp. 19-22.Xie L. A Criterion for Hurwitz Polynomials and its Applications // Modern Education and Computer Science. - 2011. - No 1. - Pp. 38-44.