Equations of Motion for Mechanical Systems

This paper deals with the description of constrained motion within the context of classical dynamics. An alternative, and simpler, proof for the recently developed new equation of motion for constrained systems is presented. The interpretation of this equation leads to new principles of analytical dynamics. We show how these results relate to Lagrange's formulation of constrained motion. New results related to the existence, uniqueness, and explicit determination of the Lagrange multipliers are provided. The approach developed herein is compared with those of Gibbs and Appell, and that of Dirac. Three examples of the application of the new equation are provided to illustrate their use.