[Orbites périodiques pour un système inélastique uni-dimensionnel de particules.]
On étudie le comportement dynamique d'un système inélastique uni-dimensionnel formé de deux particules de masses différentes se déplaçant entre deux murs. De l'énergie est ajoutée à l'un des murs, qui oscille, alors que l'autre est stationnaire. On montre que, si la particule proche du mur stationnaire est un peu plus légère que l'autre, et si les collisions entre les particules tendent vers la limite élastique, alors il y a un nombre infini d'orbites stables. On montre également que la situation couramment étudiée où les masses sont égales est un cas très particulier, dans lequel toutes les orbites sont dégénérées et tendent vers une orbit e triviale unique où l'une des particules est piégée par le mur stationnaire.
The dynamical behavior of a one-dimensional inelastic particle system with two particles of different masses traveling between two walls is investigated. Energy is added at only one of the walls, which is oscillating, while the other wall is stationary. We show that if the particle nearer to the stationary wall is slightly lighter than the other particle and collisions between particles tend to the elastic limit, there are an infinite number of stable orbits. We also show that the widely studied situation of equal masses is an extremely special case, in which all the orbits are degenerate and collapse to a single trivial orbit in which one of the particles is trapped against the stationary wall.
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@article{CRMATH_2004__339_8_603_0,
author = {Wylie, Jonathan J. and Zhang, Qiang},
title = {Periodic orbits of a one-dimensional inelastic particle system},
journal = {Comptes Rendus. Math\'ematique},
pages = {603--606},
publisher = {Elsevier},
volume = {339},
number = {8},
year = {2004},
doi = {10.1016/j.crma.2004.07.026},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.07.026/}
}
TY - JOUR AU - Wylie, Jonathan J. AU - Zhang, Qiang TI - Periodic orbits of a one-dimensional inelastic particle system JO - Comptes Rendus. Mathématique PY - 2004 SP - 603 EP - 606 VL - 339 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.07.026/ DO - 10.1016/j.crma.2004.07.026 LA - en ID - CRMATH_2004__339_8_603_0 ER -
%0 Journal Article %A Wylie, Jonathan J. %A Zhang, Qiang %T Periodic orbits of a one-dimensional inelastic particle system %J Comptes Rendus. Mathématique %D 2004 %P 603-606 %V 339 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.07.026/ %R 10.1016/j.crma.2004.07.026 %G en %F CRMATH_2004__339_8_603_0
Wylie, Jonathan J.; Zhang, Qiang. Periodic orbits of a one-dimensional inelastic particle system. Comptes Rendus. Mathématique, Tome 339 (2004) no. 8, pp. 603-606. doi : 10.1016/j.crma.2004.07.026. http://www.numdam.org/articles/10.1016/j.crma.2004.07.026/
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