A new set of equations of motion for constrained structures and a comparison of the effect of bilateral and unilateral constraints

摘要

A systematic approach is presented first, leading to a new set of equations of motion for a class of mechanical systems subject to a single frictionless contact constraint. For this, some fundamental concepts of b-geometry are utilized and adapted to the general framework of Analytical Dynamics. These concepts refer to the theory of manifolds with boundary. This boundary is defined within the original configuration manifold of the system by the unilateral constraint. After determining the essential geometric properties near the boundary, Newton's law of motion is applied. Then, the equations of motion are derived as a system of ordinary differential equations. Finally, a comparison with a formulation on systems with bilateral constraints is performed.