Vol. 6, No. 2, 2013

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ISSN: 1944-4184 (e-only)
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Dynamic impact of a particle

Jeongho Ahn and Jared R. Wolf

Vol. 6 (2013), No. 2, 147–167
Abstract

In this work, we consider a moving particle which drops down onto a stationary rigid foundation and bounces off after its contact. The equation of its motion is formulated by a second-order ordinary differential equation. The particle satisfies the Signorini contact conditions which can be interpreted in terms of complementarity conditions. The existence of weak solutions is shown by using a finite time step and the necessary a priori estimates which allow us to pass to the limit. The uniqueness of the solutions can be proved under some additional assumptions. Conservation of energy is also investigated theoretically and numerically. Numerical solutions are computed via both finite- and infinite-dimensional approaches.

Keywords
Signorini contact conditions, conservation of energy, complementarity conditions, time discretization
Mathematical Subject Classification 2010
Primary: 65L20
Secondary: 74H20
Milestones
Received: 4 October 2011
Revised: 24 April 2012
Accepted: 6 May 2012
Published: 1 September 2013

Communicated by John Baxley
Authors
Jeongho Ahn
Department of Mathematics and Statistics
Arkansas State University
P.O. Box 70
State University, AR 72467
United States
Jared R. Wolf
Department of Mathematics and Statistics
Arkansas State University
P.O. Box 70
State University, AR 72467
United States