Minimization of energy in quasi-static manipulation

Abstract

Energetic formulations of Newton's laws are valuable for mechanics problems involving multiple constraints. The following energic principle for quasistatic systems is discussed: a quasistatic system chooses that motion, from among all motions satisfying the constraints, which minimizes the instantaneous power. This minimum power principle states that a system chooses at every instant the lowest energy, or `easiest', motion in conformity with the constraints. It is shown that the principle is in general false. For example, if viscous forces act, the motion predicted by the minimum power principle will be incorrect. The authors proved that the principle is correct if there are no forces with velocity-dependent magnitude. This allows its application to many systems with Coulomb friction