Explicit Equations of Motion for Dynamical Systems with Multiple Constraints

Abstract

In this paper, we proposed a method of deriving equations of motion, which is free of Lagrange multipliers, for a constrained dynamical system with emphasis on its suitability for nonlinear nonholonomic constraints. A local coordinate space is established on the basis of a scaled acceleration-constrained flat surface and the corresponding normal space. Constraint forces are decomposed into components along this local coordinate space. The normal components of constraint forces are determined by the motion of the system and constraints, and the tangential components are arbitrary. Then Gauss' principle of least constraint is employed to minimize the tangential components so as to derive the equations of motion in explicit form. An example demonstrating the general equations derived here is provided.