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TMF, 2001, Volume 129, Number 1, Pages 31–37 (Mi tmf517)  

This article is cited in 46 scientific papers (total in 46 papers)

A New Integrable Case for the Kirchhoff Equation

V. V. Sokolov

Landau Institute for Theoretical Physics, Centre for Non-linear Studies

Abstract: A new integrable case is found for the Kirchhoff equation. The additional integral of motion is a fourth-degree polynomial, the principal metric is diagonal with the eigenvalues $a_1=a_2=1$ and $a_3=2$, and the other two metrics are nondiagonal.

DOI: https://doi.org/10.4213/tmf517

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English version:
Theoretical and Mathematical Physics, 2001, 129:1, 1335–1340

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Received: 04.06.2001

Citation: V. V. Sokolov, “A New Integrable Case for the Kirchhoff Equation”, TMF, 129:1 (2001), 31–37; Theoret. and Math. Phys., 129:1 (2001), 1335–1340

Citation in format AMSBIB
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    This publication is cited in the following articles:
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    7. P. V. Morozov, “Topology of Liouville foliations in the Steklov and the Sokolov integrable cases of Kirchhoff's equations”, Sb. Math., 195:3 (2004), 369–412  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    22. D. V. Novikov, “Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{e}(3)$”, Sb. Math., 202:5 (2011), 749–781  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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    24. Yehia H.M., Elmandouh A.A., “New conditional integrable cases of motion of a rigid body with Kovalevskaya's configuration”, J. Phys. A: Math. Theor., 44:1 (2011), 012001  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
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    40. Yehia H.M. Elmandouh A.A., “A new conditional integrable case in the dynamics of a rigid body-gyrostat”, Mech. Res. Commun., 78:A (2016), 25–27  crossref  mathscinet  isi  scopus
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    42. A. V. Tsiganov, “Bäcklund transformations for the Jacobi system on an ellipsoid”, Theoret. and Math. Phys., 192:3 (2017), 1350–1364  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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    45. R. Akbarzadeh, “The topology of isoenergetic surfaces for the Borisov–Mamaev–Sokolov integrable case on the Lie algebra $so(3,1)$”, Theoret. and Math. Phys., 197:3 (2018), 1727–1736  mathnet  crossref  crossref  adsnasa  isi  elib
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