The Maximum Dissipation Principle in Rigid-Body Dynamics with Purely Inelastic Impacts

摘要

Formulating a consistent theory for rigid-body dynamics with impacts is anintricate problem. Twenty years ago Stewart published the first consistenttheory with purely inelastic impacts and an impulsive friction model analogousto Coulomb friction. In this paper we demonstrate that the consistent impactmodel can exhibit multiple solutions with a varying degree of dissipation evenin the single-contact case. Replacing the impulsive friction model based onCoulomb friction by a model based on the maximum dissipation principle resolvesthe non-uniqueness in the single-contact impact problem. The paper constructsthe alternative impact model and presents integral equations describingrigid-body dynamics with a non-impulsive and non-compliant contact model and anassociated purely inelastic impact model maximizing dissipation. An analyticsolution is derived for the single-contact impact problem. The models are thenembedded into a time-stepping scheme. The macroscopic behaviour is compared toCoulomb friction in a large-scale granular flow problem.