In the present paper a form of equations of motion of a constrained mechanical system is constructed. These equations only contain a minimum number of accelerations. In the other words, such equations are written in independent accelerations while the configuration of the system is described by dependent coordinates. | Vietnam Journal of Mechanics, NCST of Vol. 24, 2002, No 2 (123 - 132) A FORM OF EQUATIONS OF MOTION OF CONSTRAINED MECHANICAL SYSTEMS Do SANH Hanoi University of Technology ABSTRACT. In the present paper a form of equations of motion of a constrained mechanical system is constructed. These equations only contain a minimum number of accelerations. In the other words, such equations are written in independent accelerations while the configuration of the system is described by dependent coordinates. It is important that the equations obtained are applied conveniently for . the mechanisms in which the use of independent generalized coordinates is not suitable. 1. Introduction As known [5, 6], the use of holonomic coordinates for writting equations of motion is very convenient due to simplicity. However, in the case of constrained mechanical systems including holonomic systems, for example, in the problem of dynamics of mechanisms, the choice of independent coordinates in many case is impossible (in the case of mechanisms of closed loops). Moreover, in the problem of determining dynamic reactions of kinematic joints it is necessary to introduce redundant coordinates. Such a situation is related also to multibody systems, for example, kinematics and dynamics of robotics. 2. Equations of motion of a mechanical system subjected to stationary constraints Let us consider a constrained mechanical system (holonomic and nonholonomic) of n degrees of freedom. Denote by qi , Qi (i = 1, m) the generalized coordinates and forces , respectively. In general, the generalized forces are functions of coordinates, velocities and time. Consider the system subjected to stationary constraints of the form m Lbo:i
