Energy Dissipation in Dynamical Systems Through Sequential Application and Removal of Constraints

Abstract

A strategy to remove energy from finite-dimensional elastic systems is presented. The strategy is based on the cyclic application and removal of constraints that effectively remove and restore degrees of freedom of the system. In general, application of a constraint removes kinetic energy from the system, while removal of the constraint resets the system for a new cycle of constraint application. Conditions that lead to a net loss in kinetic energy per cycle and bounds on the amount of energy removed are presented. In linear systems, these bounds are related to the modes of the system in its two states, namely, with and without constraints. It is shown that energy removal is always possible, even using a random switching schedule, except in one scenario, when energy is trapped in modes that span an invariant subspace with special orthogonality properties. Applications to nonlinear systems are discussed. Examples illustrate the process of energy removal in both linear and nonlinear systems.