K. P. Hadeler, E. N. Selivanova, “On the Case of Kovalevskaya and New Examples of Integrable Conservative Systems on $S^2$”, Regul. Chaotic Dyn., 4:3 (1999), 45

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Regular and Chaotic Dynamics, 1999, Volume 4, Issue 3, Pages 45–52
DOI: https://doi.org/10.1070/RD1999v004n03ABEH000115 (Mi rcd911)

This article is cited in 9 scientific papers (total in 9 papers)

On the Case of Kovalevskaya and New Examples of Integrable Conservative Systems on

S^{2}

$S^2$

K. P. Hadeler^a, E. N. Selivanova^b

^a Mathematische Fakultät, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
^b Department of Geometry, Nizhny Novgorod State Pedagogical University, 603000 Russia, Nizhny Novgorod, ul. Ulyanova 1

Citations (9)

DOI: https://doi.org/10.1070/RD1999v004n03ABEH000115

Abstract: There is a well-known example of an integrable conservative system on

S^{2}

$S^2$ , the case of Kovalevskaya in the dynamics of a rigid body, possessing an integral of fourth degree in momenta. The aim of this paper is to construct new families of examples of conservative systems on

S^{2}

$S^2$ possessing an integral of fourth degree in momenta.

Received: 06.01.1999

Bibliographic databases:

Document Type: Article

MSC: 34C40, 58F05, 58F07, 58D17, 70E15

Language: English

Citation: K. P. Hadeler, E. N. Selivanova, “On the Case of Kovalevskaya and New Examples of Integrable Conservative Systems on

S^{2}

$S^2$ ”, Regul. Chaotic Dyn., 4:3 (1999), 45–52

Citation in format AMSBIB

\Bibitem{HadSel99}

\by K. P. Hadeler, E. N. Selivanova

\paper On the Case of Kovalevskaya and New Examples of Integrable Conservative Systems on $S^2$

\jour Regul. Chaotic Dyn.

\yr 1999

\vol 4

\issue 3

\pages 45--52

\mathnet{http://mi.mathnet.ru/rcd911}

\crossref{https://doi.org/10.1070/RD1999v004n03ABEH000115}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1777879}

\zmath{https://zbmath.org/?q=an:1012.37037}

Linking options:

https://www.mathnet.ru/eng/rcd911

https://www.mathnet.ru/eng/rcd/v4/i3/p45

This publication is cited in the following 9 articles:

Szuminski W., Maciejewski A.J., “Comment on “on the Integrability of 2D Hamiltonian Systems With Variable Gaussian Curvature” By a. a. Elmandouh”, Nonlinear Dyn., 104:2 (2021), 1443–1450
Borisov A. Mamaev I., “Rigid Body Dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520
Leo T. Butler, Lagrangian Mechanics, 2017
Galliano Valent, “On a Class of Integrable Systems with a Quartic First Integral”, Regul. Chaotic Dyn., 18:4 (2013), 394–424
Anton Galajinsky, Olaf Lechtenfeld, “On two-dimensional integrable models with a cubic or quartic integral of motion”, J. High Energ. Phys., 2013:9 (2013)
Hamad M Yehia, “A new 2D integrable system with a quartic second invariant”, J. Phys. A: Math. Theor., 45:39 (2012), 395209
H M Yehia, “The master integrable two-dimensional system with a quartic second integral”, J. Phys. A: Math. Gen., 39:20 (2006), 5807
A V Tsiganov, “A new integrable system onS2with the second integral quartic in the momenta”, J. Phys. A: Math. Gen., 38:16 (2005), 3547
K. P. Hadeler, Johannes Müller, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, 2001, 311

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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