EQUATIONS OF MOTION FOR CONSTRAINED MECHANICAL SYSTEMS WITH SPECIAL SELECTION OF QUASI-VELOCITIES

This paper presents the general form of explicit equations of motion for a mechanical system of particles subjected to holonomic and (or) nonholonomic constraints using Gibbs-Appell method. The equations of motion are derived directly and there is no need to evaluate the Gibbs function. Also general method is presented to select quasi-velocities which satisfy all constraints, eliminate Lagrange multipliers and reduce the number of equations. This method is applicable in the presence of both ideal and nonideal constraints. Finally, two examples are presented to demonstrate the use of general equations.

Keywords:

Explicit equations of motion , Gibbs-Appell function , non-holonomic constraints , eliminate Lagrangian multiplier , constrained quasi-velocities