Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8418Research ArticleConstructing Dynamic Equations of Constrained Mechanical SystemsDeressa Chernet Tuge-Department of Mathematicschernettuge@ymail.comJimma University1503201339210408092016Copyright © 2013,2013In this paper constructing equation of mechanical systems based on their kinetic energy, potential energy and dissipative force is discussed. Both the holonomic and non-holonomic constraints are considered. Equations of constraint forces resulting from ideal and non-ideal nature of the constraints are developed.It is shown that, the constraint force is a sum of two forces resulting from the ideal and non-ideal nature of the constraints. An explicit equation of the acceleration of the system is developed basing on the constraint forces from the nature of the constraints. For investigating the deviation of the system from the trajectory of the constraint equations, excess variables are included in the equations of the constraints. The stability of the system is based on determining the sign of constants emerging from developing the Lagrange’s equation of motion for the constraints. The determination of the sign of the constants is made based on Routh-Hurwitz Criterion for Stability. An example is used to demonstrate each of the equations developed in the paper and constructing state-space equation of the system.dissipative forceexcess variablesideal constraintsLagrange equationnon-ideal constraintsstabilityRouth-Hurwitz criterion for stabilitystate-space equationизбыточные переменныеидеальные связинеидеальные связиустойчивостькритерий Рауса–Гурвицапространство состоянийфункция Лагранжадиссипативная функция[Mukharlyamov R.G. Stabilization of the Motions of Mechanical Systems in Prescribed Phase-Space Manifolds // Applied Mathematics and Mechanics. — 2006. — Vol. 70. — Pp. 210–222.][Udwadia F.E. Recent Advances in Multi-body Dynamics and Nonlinear Control // J. of the Braz. Soc. of Mech. Sci. & Eng. — 2006. — Vol. XXVIII, No 3 / 311. — Pp. 311–314.][Udwadia F.E., Kalaba R.E. On the Foundation of Analytical Dynamics // International Journal of Nonlinear Mechanics. — 2002. — Vol. 37. — Pp. 1079–1090.][Dorf R.C., Bishop R.H. Modern Control Systems. — 12th edition. edition. — Prentice Hall, 2011.][Norman S.N. Control Systems Engineering. — 6th edition edition. — John Wiley & Sons, Inc, 2011.][Amirouche F. Fundamentals of Multibody Dynamics: Theory and Applications. — Boston: Birkh.auser, 2006.][Gonzalez F., Kovecses J. Use of Penalty Formulations in Dynamic Simulation and Analysis of Redundantly Constrained Multibody Systems // Multibody System Dynamics. — 2012.][Blajer W. Advanced Design of Mechanical Systems: From Analysis to Optimization. — New York: Springer Wien, 2009.]