Dynamics in the Kepler problem on the Heisenberg group Full article
| Journal |
Analysis and Mathematical Physics
ISSN: 1664-2368 , E-ISSN: 1664-235X |
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| Output data | Year: 2024, Volume: 14, Number: 3, Article number : 58, Pages count : 15 DOI: 10.1007/s13324-024-00921-2 | ||||
| Tags | Heisenberg group · Kepler problem · Nonholonomic dynamics · Almost Poisson bracket · First integral | ||||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
| 2 | Mathematical Center in Akademgorodok | 075-15-2022-282 |
Abstract:
We study the nonholonomic motion of a point particle on th eHeisenberg group around the fixed “sun” placed at the origin whose potential is given by the fundamental solution of the sub-Laplacian. In contrast with several recent papers that approach this problem as a variational one (hence a control problem) we study the equations of dynamical motion which are non-variational in nonholonomic mechanics. We find three independent first integrals of the system and show that its bounded trajectories are wound up around certain surfaces of the fourth order. We also describe some particular cases of trajectories.
Cite:
Basalaev S.
, Agapov S.
Dynamics in the Kepler problem on the Heisenberg group
Analysis and Mathematical Physics. 2024. V.14. N3. 58 :1-15. DOI: 10.1007/s13324-024-00921-2 WOS Scopus РИНЦ OpenAlex
Dynamics in the Kepler problem on the Heisenberg group
Analysis and Mathematical Physics. 2024. V.14. N3. 58 :1-15. DOI: 10.1007/s13324-024-00921-2 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Nov 27, 2023 |
| Accepted: | Apr 17, 2024 |
| Published print: | May 11, 2024 |
| Published online: | May 11, 2024 |
Identifiers:
| Web of science: | WOS:001219691700001 |
| Scopus: | 2-s2.0-85192985300 |
| Elibrary: | 67490584 |
| OpenAlex: | W4396833988 |
Citing:
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