The geometry of dissipation

Abstract

Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative systems to dissipative systems, specially those concerning the symmetries and integrability of these systems. More specifically, three classes of geometric frameworks modelling dissipative systems are considered: systems with external forces, contact systems and systems with impacts. The first two allow modelling a continuous dissipation of energy over time, while the latter also permits considering abrupt changes of energy in the instants of the impacts.