A Variational Principle for Quasistatic Mechanics

Quasistatic mechanical systems are those in which mass or acceleration are sufficientlysmall that the inertial term mu in F = mu is negligible compared to dissipative forces. In roboticsquasistatic mechanics may be used for systems with friction when motions are sufficiently slow. Here weconsider a general quasistatic system with constraints and both dissipative and conservative forces.Under some conditions it is possible to replace Newton's law with the simple and intuitive variationalprinciple that the system moves within the space of unconstrained motions, in such a way as to minimizepower. For quasistatic systems we find that this principle of minimum power is correct if all thevelocity-dependent forces are parallel to the velocity and have a magnitude independent of velocity, i.e.are essentially equivalent to Coulomb friction. No restriction need be imposed on velocity-independentforces or forces of constraint.