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

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Abstract

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 theG 2 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.

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Authors and Affiliations

  1. Leningrad Branch of V. A. Steklov Mathematical Institute, SU-191011, Leningrad, USSR

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

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  1. A. G. Reyman
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  2. M. A. Semenov-Tian-Shansky
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Communicated by Ya. G. Sinai

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Reyman, A.G., Semenov-Tian-Shansky, M.A. A new integrable case of the motion of the 4-dimensional rigid body. Commun.Math. Phys. 105, 461–472 (1986). https://doi.org/10.1007/BF01205938

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  • DOI: https://doi.org/10.1007/BF01205938

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