UDC 531.3 Constructing Dynamic Equations of Constrained Mechanical Systems Chernet Tuge Deressa Department of Mathematics Jimma University Jimma, Ethiopia In 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. <...> 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. <...> Key words and phrases: dissipative force, excess variables, ideal constraints, Lagrange equation, non-ideal constraints, stability, Routh-Hurwitz criterion for stability, state-space equation. 1. <...> Introduction In an article by R.G. Mukharlyamov [1], constructing equation of mechanical system when the kinetic energy, potential energy and dissipative forces are known is detailed. <...> Both holonomic and non-holonomic constraints are considered. <...> All the discussions made by R.G. Mukharlyamov in [1] were for Ideal constraints. <...> In an article by Udwadia F. [2, 3] constructing equation of mechanical system involving both the ideal and non-ideal constraints is discussed. <...> The method detailed is so general that it makes the ideal constraints only a particular case. <...> The issue of constraint stabilization is not included in Udwadia F. The idea for developing this paper is mainly an insight from investigating the above two articles. <...> In this paper, firstly, a new idea of developing equation of mechanical system simultaneously from Lagrange’s equation of motion for a constrained mechanical system and Lagrange’s equation of motion for the constraints is discussed. <...> In other words dynamic equation for the constraints is developed and is used for investigation of asymptotic stability of the system. <...> Secondly, the equation of a constraint force generated as a result of constraining a system is developed. <...> In constructing <...>