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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 151, Number 1, Pages 26–43
DOI: https://doi.org/10.4213/tmf6009 (Mi tmf6009) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Compatible Lie–Poisson brackets on the Lie algebras $e(3)$ and $so(4)$

A. V. Tsiganov

St. Petersburg State University, Faculty of Physics
Full-text PDF (493 kB) Citations (10)
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DOI: https://doi.org/10.4213/tmf6009
Abstract: We completely classify the compatible Lie–Poisson brackets on the dual spaces of the Lie algebras $e(3)$ and $so(4)$. The corresponding bi-Hamiltonian systems are the spinning tops corresponding to the classical cases of integrability of the Euler equations, the Kirchhoff equations, and the Poincaré–Zhukovskii equations.
Keywords: integrable system, bi-Hamiltonian manifold, Lie–Poisson tensor.
Received: 03.07.2006
Revised: 12.10.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 151, Issue 1, Pages 459–473
DOI: https://doi.org/10.1007/s11232-007-0034-z
Bibliographic databases:
Language: Russian
Citation: A. V. Tsiganov, “Compatible Lie–Poisson brackets on the Lie algebras $e(3)$ and $so(4)$”, TMF, 151:1 (2007), 26–43; Theoret. and Math. Phys., 151:1 (2007), 459–473
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:65
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