Dynamics of Dissipative Systems with Hamiltonian Structures

Abstract

In this work, we study a class of dissipative, nonsmooth [Formula: see text] degree-of-freedom dynamical systems. As the dissipation is assumed to be proportional to the momentum, the dynamics in such systems is conformally symplectic, allowing us to use some of the Hamiltonian structure. We initially show that there exists an integral invariant of the Poincaré–Cartan type in such systems. Then, we prove the existence of a generalized Liouville Formula for conformally symplectic systems with rigid constraints using the integral invariant. A two degree-of-freedom system is analyzed to support the relevance of our results.