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Dynamics in the Kepler problem on the Heisenberg group. / Basalaev, Sergey; Agapov, Sergei.

In: Analysis and Mathematical Physics, Vol. 14, No. 3, 58, 06.2024.

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

Harvard

Basalaev, S & Agapov, S 2024, 'Dynamics in the Kepler problem on the Heisenberg group', Analysis and Mathematical Physics, vol. 14, no. 3, 58. https://doi.org/10.1007/s13324-024-00921-2

APA

Basalaev, S., & Agapov, S. (2024). Dynamics in the Kepler problem on the Heisenberg group. Analysis and Mathematical Physics, 14(3), [58]. https://doi.org/10.1007/s13324-024-00921-2

Vancouver

Basalaev S, Agapov S. Dynamics in the Kepler problem on the Heisenberg group. Analysis and Mathematical Physics. 2024 Jun;14(3):58. doi: 10.1007/s13324-024-00921-2

Author

Basalaev, Sergey ; Agapov, Sergei. / Dynamics in the Kepler problem on the Heisenberg group. In: Analysis and Mathematical Physics. 2024 ; Vol. 14, No. 3.

BibTeX

@article{a45e225444e4451293976408b4ca5da4,
title = "Dynamics in the Kepler problem on the Heisenberg group",
abstract = "We study the nonholonomic motion of a point particle on the Heisenberg 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.",
keywords = "37J60, 37N05, 53C17, 70F25, Almost Poisson bracket, First integral, Heisenberg group, Kepler problem, Nonholonomic dynamics",
author = "Sergey Basalaev and Sergei Agapov",
note = "The work of the first author is supported by the Mathematical Center in Akademgorodok under the Agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation. The work of the second author was performed according to the Government research assignment for IM SB RAS, Project No. FWNF-2022-0004.",
year = "2024",
month = jun,
doi = "10.1007/s13324-024-00921-2",
language = "English",
volume = "14",
journal = "Analysis and Mathematical Physics",
issn = "1664-2368",
publisher = "Springer Science + Business Media",
number = "3",

}

RIS

TY - JOUR

T1 - Dynamics in the Kepler problem on the Heisenberg group

AU - Basalaev, Sergey

AU - Agapov, Sergei

N1 - The work of the first author is supported by the Mathematical Center in Akademgorodok under the Agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation. The work of the second author was performed according to the Government research assignment for IM SB RAS, Project No. FWNF-2022-0004.

PY - 2024/6

Y1 - 2024/6

N2 - We study the nonholonomic motion of a point particle on the Heisenberg 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.

AB - We study the nonholonomic motion of a point particle on the Heisenberg 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.

KW - 37J60

KW - 37N05

KW - 53C17

KW - 70F25

KW - Almost Poisson bracket

KW - First integral

KW - Heisenberg group

KW - Kepler problem

KW - Nonholonomic dynamics

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85192985300&origin=inward&txGid=f99b81aac83edb714fc140e80ac6c36f

UR - https://www.mendeley.com/catalogue/02a5d774-b834-3ba0-8f66-641ca209a0bd/

U2 - 10.1007/s13324-024-00921-2

DO - 10.1007/s13324-024-00921-2

M3 - Article

VL - 14

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

SN - 1664-2368

IS - 3

M1 - 58

ER -

ID: 60875203