UDC 531.3 Dynamic Equation of Constrained Mechanical System A. W. Beshaw Department of Mathematics Bahir Dar University Bahir Dar, Ethiopia This paper modifies an explicit dynamic equation of constrained mechanical system. <...> The equations of motion in the form of the Lagrange equations with undetermined multipliers are constructed based on d’Alambert–Lagrange’s principle. <...> Expressions for the undetermined multipliers are defined by considering the possible deviations from the constraints equations. <...> For constraints stabilization additional variables used to estimate the deviations caused by errors in the initial conditions and the use of numerical methods. <...> For approximation of ordinary differential equations solution, in particular, the nonlinear equations of first order, use explicit numerical methods. <...> Stability with respect to initial deviations from the constraints equations and stabilization of the numerical solution depend on the values of the elements of this matrix. <...> As a result values for the matrix of coefficients corresponding to the solution of the dynamics equations by the method of Euler and fourth order Runge–Kutta method are defined. <...> Suggested method for solving the problem of stabilization is used for modeling of the disk motion on a plane without slipping. <...> Key words and phrases: unconstrained system, holonomic constraints, nonholonomic constraints, stabilization, Taylor series, numerical solution. 1. <...> When the configuration coordinates (u1,u2, . . . ,uN) are not all independent variables, a set of reduced-order variables q = (q1, q2, . . . , qn) exists, where n < N, that is sufficient to define a system configuration [2]. <...> Now let us consider the system as unconstrained whose configuration is described (1) ponents ˙qi of the velocity of the system can be assigned independently at any given initial time, say t = t0. <...> The equation of motion of the system can be obtained, using Lagrange equation Received 26th June, 2014. <...> When we say the Mechanical system is unconstrained, we mean that the com 116 Bulletin of PFUR. <...> The equation of motion of the system (2) can be rewritten by a matrix and f = f(q, ˙q, t) is an n Ч 1 column array of generalized applied forces and generalized inertia force terms (including the so-called “centrifugal” and “Coriolis” q = f, where M is an nЧn <...>