UDC 531.3 On Solving Differential Kinematic Equations for Constrained Mechanical Systems A. W. Beshaw Department of Mathematics Bahr Dar University Ethiopia, Bahr Dar This 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 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. <...> Key words and phrases: kinematic constraints, pseudo-inverse, approximate solution, stability, Euler’s method, Runge-Kutta methods. 1. <...> Introduction ordinates q1, q2, . . . , qn and dependent velocities ˙q1, ˙q2, · · · , ˙qn described by the system of ordinary differential equations [1]: q˙ = v(q, t), q˙ = dq dt , q ∈ Rn, Let the kinematic state of a mechanical system be determined by the position co(1) where v is a vector valued function and we shall assume that the function v together with its first partial derivatives are continuous in some domain D ⊂ Rn ЧR. <...> And assume that the system is subjected to m holonomic constraints: f(q, t) = 0, where, f ∈ Rm, m n f(q0, t0) = 0. (2) (3) then it is usually assumed that the initial values of the coordinates also exactly satisfy the constraint equations (4) As stated in [2] relations (1) should be constructed according to the constraint equations (3), which under relations (4), form a set of particular integrals of the system of differential equations (1). <...> Solution of systems of differential equations can be rewritten as The equation (5); the system ofmordinary <...>