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Dynamic impact of
a particle
Jeongho Ahn and Jared R. Wolf
Vol. 6 (2013), No. 2, 147–167
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 65L20
Secondary: 74H20
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Milestones
Received: 4 October 2011
Revised: 24 April 2012
Accepted: 6 May 2012
Published: 1 September 2013
Communicated by John Baxley
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Authors |
| Jeongho Ahn | |
| Department of Mathematics and
Statistics Arkansas State University P.O. Box 70 State University, AR 72467 United States |
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| Jared R. Wolf | |
| Department of Mathematics and
Statistics Arkansas State University P.O. Box 70 State University, AR 72467 United States |
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