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A New Integrable Case for the Kirchhoff Equation

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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.

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REFERENCES

  1. V. A. Steklov, On the Motion of a Rigid Body in a Fluid [in Russian], Press Adolf Darre, Kharkov (1893).

    Google Scholar 

  2. V. V. Kozlov, Symmetries, Topology, and Resonances in Hamiltonian Mechanics [in Russian], Udmurdski State Univ., Izhevsk (1995).

    Google Scholar 

  3. S. P. Novikov, Russ. Math. Surv., 37, 1 (1982).

    Google Scholar 

  4. T. Wolf and A. Brand, The Computer Algebra Package CRACK for Investigating PDEs (http://www.unikoeln. de/REDUCE/3.6/doc/crack/) (1992).

  5. A. P. Veselov, Sov. Math. Dokl., 27, 740 (1983).

    Google Scholar 

  6. M. Adler and P. van Moerbeke, Commun. Math. Phys., 113, 659 (1988).

    Google Scholar 

  7. M. Adler and P. van Moerbeke, Adv. Math. Suppl. Stud., 9, 81 (1986).

    Google Scholar 

  8. A. G. Reyman and M. A. Semenov-Tian-Shansky, Commun. Math. Phys., 105, 461 (1986).

    Google Scholar 

  9. A. I. Bobenko, A. G. Reyman, and M. A. Semenov-Tian-Shansky, Commun. Math. Phys., 122, 321 (1989).

    Google Scholar 

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Authors and Affiliations

  1. Center for Nonlinear Investigations, Landau Institute for Theoretical Physics, RAS, Moscow, Russia

    V. V. Sokolov

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  1. V. V. Sokolov
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Sokolov, V.V. A New Integrable Case for the Kirchhoff Equation. Theoretical and Mathematical Physics 129, 1335–1340 (2001). https://doi.org/10.1023/A:1012411326312

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  • DOI: https://doi.org/10.1023/A:1012411326312

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