Billiard dynamics of bouncing dumbbell

Y. Baryshnikov; V. Blumen; K. Kim; V. Zharnitsky

doi:10.1016/j.physd.2013.11.007

Billiard dynamics of bouncing dumbbell

Y. Baryshnikov, V. Blumen, K. Kim, V. Zharnitsky

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	21-27
Number of pages	7
Journal	Physica D: Nonlinear Phenomena
Volume	269
DOIs	https://doi.org/10.1016/j.physd.2013.11.007
State	Published - Feb 15 2014

Keywords

Adiabatic invariant
Billiard dynamics
Bouncing dumbbell

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Online availability

10.1016/j.physd.2013.11.007

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abstract = "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.",

keywords = "Adiabatic invariant, Billiard dynamics, Bouncing dumbbell",

author = "Y. Baryshnikov and V. Blumen and K. Kim and V. Zharnitsky",

note = "Funding Information: The authors acknowledge support from National Science Foundation grant DMS 08-38434 EMSW21-MCTP : “Research Experience for Graduate Students”. YMB and VZ were also partially supported by NSF grant DMS-0807897 . YMB and VB were also partially supported by ONR . The authors would also like to thank Mark Levi for a helpful discussion.",

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AU - Blumen, V.

AU - Kim, K.

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Y1 - 2014/2/15

N2 - 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.

AB - 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.

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Billiard dynamics of bouncing dumbbell

Abstract

Keywords

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