Communications in Mathematical Physics

, Volume 105, Issue 3, pp 461–472 | Cite as

A new integrable case of the motion of the 4-dimensional rigid body

  • A. G. Reyman
  • M. A. Semenov-Tian-Shansky


A Lax pair for a new family of integrable systems on SO(4) is presented. The construction makes use of a twisted loop algebra of theG2 Lie algebra. We also describe a general scheme producing integrable cases of the generalized rigid body motion in an external field which have a Lax representation with spectral parameter. Several other examples of multi-dimensional tops are discussed.


Neural Network Nonlinear Dynamics Rigid Body Integrable System General Scheme 
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • A. G. Reyman
    • 1
  • M. A. Semenov-Tian-Shansky
    • 1
  1. 1.Leningrad Branch of V. A. Steklov Mathematical InstituteLeningradUSSR

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