Billiard dynamics of bouncing dumbbell

A system of two masses connected with a weightless rod (called dumbbell in this paper) interacting with a flat boundary is considered. The sharp bound on the number of collisions with the boundary is found using billiard techniques. In case the ratio of masses is large and the dumbbell rotates fast,...

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Bibliographic Details
Published in:Physica. D 2014-02, Vol.269, p.21-27
Main Authors: Baryshnikov, Y., Blumen, V., Kim, K., Zharnitsky, V.
Format: Article
Language:English
Subjects:
Adiabatic invariant
Billiard dynamics
Bouncing
Bouncing dumbbell
Boundaries
Collisions
Dynamical systems
Invariants
Microgravity
Nonlinear dynamics
Sporting goods
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Summary:A system of two masses connected with a weightless rod (called dumbbell in this paper) interacting with a flat boundary is considered. The sharp bound on the number of collisions with the boundary is found using billiard techniques. In case the ratio of masses is large and the dumbbell rotates fast, an adiabatic invariant is obtained. •We study dynamics of a system of two masses connected with a weightless rod, which we call a dumbbell system.•The dumbbell interacts with a flat boundary.•We obtain a sharp bound on the number of bounces using billiard techniques.•In case the ratio of masses is large and the dumbbell rotates fast we find an adiabatic invariant.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2013.11.007