Journal of Nonlinear Mathematical Physics

Volume 27, Issue 1, October 2019, Pages 162 - 169

SO(4)-symmetry of mechanical systems with 3 degrees of freedom

Authors
Sofiane Bouarroudj
New York University Abu Dhabi, Division of Science and Mathematics, P.O. Box 129188, United Arab Emirates,sofiane.bouarroudj@nyu.edu
Semyon E. Konstein*
I.E.Tamm department of Theoretical Physics, P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Leninskij prosp. 53, RU-119991 Moscow, Russia,konstein@lpi.ru
*Corresponding author
Corresponding Author
Semyon E. Konstein
Received 30 May 2019, Accepted 20 July 2019, Available Online 25 October 2019.
DOI
10.1080/14029251.2020.1683997How to use a DOI?
Abstract

We answered an old question: does there exist a mechanical system with 3 degrees of freedom, except for the Coulomb system, which has 6 first integrals generating the Lie algebra 𝔬(4) by means of the Poisson brackets? A system which is not centrally symmetric, but has 6 first integrals generating Lie algebra 𝔬(4), is presented. It is shown also that not every mechanical system with 3 degrees of freedom has first integrals generating 𝔬(4).

Copyright
Β© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 1
Pages
162 - 169
Publication Date
2019/10/25
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1683997How to use a DOI?
Copyright
Β© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Sofiane Bouarroudj
AU  - Semyon E. Konstein
PY  - 2019
DA  - 2019/10/25
TI  - SO(4)-symmetry of mechanical systems with 3 degrees of freedom
JO  - Journal of Nonlinear Mathematical Physics
SP  - 162
EP  - 169
VL  - 27
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1683997
DO  - 10.1080/14029251.2020.1683997
ID  - Bouarroudj2019
ER  -