Continuous orbit transitions in a one-dimensional inelastic particle system

Rong Yang; Jonathan J. Wylie

doi:10.1016/j.crma.2010.04.016

Mathematical Problems in Mechanics

Continuous orbit transitions in a one-dimensional inelastic particle system

Presented by: Philippe G. Ciarlet

Rong Yang ¹; Jonathan J. Wylie ^2,³

¹ Joint Advanced Research Center of University of Science and Technology of China and City University of Hong Kong, Suzhou, Jiangsu, China
² Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
³ Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA

Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 593-595.

Abstract
Résumé

Continuous transitions between different periodic orbits in a one-dimensional inelastic particle system with two particles are investigated. We explain why continuous transitions that occur when adding or subtracting a single collision are, generically, of co-dimension 2. However, we show that there are an infinite set of degenerate transitions of co-dimension 1. We provide an analysis that gives a simple criteria to classify which transitions are degenerated purely from the discrete set of collisions that occur in the orbits.

Nous étudions les transitions continues entre différentes orbites périodiques dans un système unidimensionnel inélastique à deux particules. Nous expliquons pourquoi les transitions continues qui apparaissent lorsque l'on ajoute ou enlève une collision sont, en général, de codimension 2. Cependant, nous montrons qu'il existe un ensemble infini de transitions dégénérées de codimension 1. Nous fournissons une méthode qui, en se basant uniquement sur l'ensemble des collisions qui interviennent dans les orbites, donne un critère simple pour déterminer quelles transitions sont dégénérées.

Received: 2010-03-09
Accepted: 2010-03-23
Published online: 2010-04-24

DOI: 10.1016/j.crma.2010.04.016

Author's affiliations:

Rong Yang ¹; Jonathan J. Wylie ^{2, 3}

¹ Joint Advanced Research Center of University of Science and Technology of China and City University of Hong Kong, Suzhou, Jiangsu, China
² Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
³ Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA

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     author = {Rong Yang and Jonathan J. Wylie},
     title = {Continuous orbit transitions in a one-dimensional inelastic particle system},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {593--595},
     publisher = {Elsevier},
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     number = {9-10},
     year = {2010},
     doi = {10.1016/j.crma.2010.04.016},
     language = {en},
}

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Rong Yang; Jonathan J. Wylie. Continuous orbit transitions in a one-dimensional inelastic particle system. Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 593-595. doi : 10.1016/j.crma.2010.04.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.04.016/

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