Dynamics in the Kepler problem on the Heisenberg group

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...

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Veröffentlicht in:Analysis and mathematical physics 2024-06, Vol.14 (3), Article 58
Hauptverfasser: Basalaev, Sergey, Agapov, Sergei
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-024-00921-2