Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 359, Issue 1789, Pages 2467-2482Publisher
ROYAL SOC LONDON
DOI: 10.1098/rsta.2001.0904
Keywords
rigid bodies; elastic bodies; impulses; Coulomb friction
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In this paper, the continuous and numerical formulations of rigid-body dynamics based on measure differential inclusions and time-stepping methods recently developed are described and extended to include a finite number of elastic modes of vibration. The time-stepping methods already incorporate Coulomb friction, and are able to handle situations such as Painleve's famous problem where impulsive forces occur without a collision. The elastic modes of vibration can be incorporated directly into the continuous formulation, but due to the stiffness typical of elastic vibrations, the numerical methods used need to be modified to incorporate them directly. The resulting numerical methods are dissipative in the limit, but only dissipate energy while there is contact.
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