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Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem
Репозиторій DSpace/Manakin
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem
Інший ID:
2010 Mathematics Subject Classification: 37J15; 37J35; 70H06; 70H33
DOI:10.3842/SIGMA.2016.010
DOI:10.3842/SIGMA.2016.010
Посилання:
Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem / J.F. Cariñena, M.F. Rañada // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Analytical Mechanics and Dif ferential Geometry in honour
of Sergio Benenti. The full collection is available at http://www.emis.de/journals/SIGMA/Benenti.html.
This work has been supported by the research projects MTM–2012–33575 (MICINN, Madrid)
and DGA-E24/1 (DGA, Zaragoza).
Дата:
2016
Переглядів:
643
Завантажень:
167
Анотація:
The existence of quasi-bi-Hamiltonian structures for the Kepler problem is studied. We first relate the superintegrability of the system with the existence of two complex functions endowed with very interesting Poisson bracket properties and then we prove the existence of a quasi-bi-Hamiltonian structure by making use of these two functions. The paper can be considered as divided in two parts. In the first part a quasi-bi-Hamiltonian structure is obtained by making use of polar coordinates and in the second part a new quasi-bi-Hamiltonian structure is obtained by making use of the separability of the system in parabolic coordinates.
