Journal article
Convolution complementarity problems with application to impact problems
IMA journal of applied mathematics, Vol.71(1), pp.92-119
2006
DOI: 10.1093/imamat/hxh087
Abstract
Convolution complementarity problems (CCPs) have the following form: given a matrix-valued function k and a vector-valued function q, find a vector-valued function u satisfying 0 ≤ u(t) ⊥ (k * u)(t) + q(t) ≥ 0 for all t. In this paper CCPs are applied to a mechanical impact problem, but they can also be applied to other dynamic problems with hard constraints. CCPs are shown to have solutions provided q(0) ≥ 0 and q is sufficiently regular, k has locally bounded variation and k(0+) is a P-matrix. Uniqueness also holds provided, in addition, k(0+) is symmetric positive definite. This theory shows that the impact problem studied here has a unique solution, and that energy is conserved. Numerical methods have been devised and implemented for the impact problem, and the results are presented. © The Author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Details
- Title: Subtitle
- Convolution complementarity problems with application to impact problems
- Creators
- David E Stewart - University of Iowa
- Resource Type
- Journal article
- Publication Details
- IMA journal of applied mathematics, Vol.71(1), pp.92-119
- Publisher
- Oxford University Press
- DOI
- 10.1093/imamat/hxh087
- ISSN
- 0272-4960
- eISSN
- 1464-3634
- Language
- English
- Date published
- 2006
- Academic Unit
- Mathematics
- Record Identifier
- 9984241153602771
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