The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere
Publication type: Journal Article
Publication date: 2013-05-01
scimago Q3
wos Q3
SJR: 0.312
CiteScore: 1.9
Impact factor: 0.8
ISSN: 15603547, 14684845
Mathematics (miscellaneous)
Abstract
In this paper, we investigate the dynamics of systems describing the rolling without slipping and spinning (rubber rolling) of various rigid bodies on a plane and a sphere. It is shown that a hierarchy of possible types of dynamical behavior arises depending on the body’s surface geometry and mass distribution. New integrable cases and cases of existence of an invariant measure are found. In addition, these systems are used to illustrate that the existence of several nontrivial involutions in reversible dissipative systems leads to quasi-Hamiltonian behavior.
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Metrics
83
Total citations:
83
Citations from 2024:
6
(7%)
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GOST
Copy
Borisov A. V. et al. The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere // Regular and Chaotic Dynamics. 2013. Vol. 18. No. 3. pp. 277-328.
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Borisov A. V., Mamaev I. S., Bizyaev I. A. The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere // Regular and Chaotic Dynamics. 2013. Vol. 18. No. 3. pp. 277-328.
Cite this
RIS
Copy
TY - JOUR
DO - 10.1134/s1560354713030064
UR - https://doi.org/10.1134/s1560354713030064
TI - The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere
T2 - Regular and Chaotic Dynamics
AU - Borisov, Alexey V.
AU - Mamaev, Ivan S.
AU - Bizyaev, Ivan A.
PY - 2013
DA - 2013/05/01
PB - Pleiades Publishing
SP - 277-328
IS - 3
VL - 18
SN - 1560-3547
SN - 1468-4845
ER -
Cite this
BibTex (up to 50 authors)
Copy
@article{2013_Borisov,
author = {Alexey V. Borisov and Ivan S. Mamaev and Ivan A. Bizyaev},
title = {The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere},
journal = {Regular and Chaotic Dynamics},
year = {2013},
volume = {18},
publisher = {Pleiades Publishing},
month = {may},
url = {https://doi.org/10.1134/s1560354713030064},
number = {3},
pages = {277--328},
doi = {10.1134/s1560354713030064}
}
Cite this
MLA
Copy
Borisov, Alexey V., et al. “The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere.” Regular and Chaotic Dynamics, vol. 18, no. 3, May. 2013, pp. 277-328. https://doi.org/10.1134/s1560354713030064.