Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 465, Issue 2101, Pages 1-23Publisher
ROYAL SOC
DOI: 10.1098/rspa.2008.0079
Keywords
impulse methods; Darboux-Keller's dynamics; stiff problem
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Funding
- National Science Foundation of China [10772002]
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Part I of this paper develops a framework that is an extension of the Darboux-Keller shock dynamics towards frictionless multiple impacts between bodies composed of rate-independent materials. A numerical algorithm is proposed in this paper, in which the impulsive differential equation is discretized with respect to the primary impulse corresponding to the contact with the highest potential energy, and the integration step size is estimated at the momentum level. This algorithm respects the energetic constraints and avoids the stiff ordinary differential equation problem arising by directly using the compliant model. The well-known example of Newton's cradle, as well as Bernoulli's system, is used to illustrate the developments.
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