On the Lax pairs for the generalized Kowalewski and Goryachev-Chaplygin tops

Abstract

A polynomial deformation of the Kowalewski top is considered. This deformation includes as a degeneration a new integrable case for the Kirchhoff equations found recently by one of the authors. A $5\times 5$ matrix Lax pair for the deformed Kowalewski top is proposed. Also deformations of the two-field Kowalewski gyrostat and the $so(p,q)$ Kowalewski top are found. All our Lax pairs are deformations of the corresponding Lax representations found by Reyman and Semenov-Tian {S}hansky. In addition, a similar deformation of the Goryachev-Chaplygin top and its $3\times 3$ matrix Lax representation is constructed.

arXiv comment9 pages, LaTeX, with corrections

Cited by in corpus (6)

• Poisson maps and integrable deformations of Kowalevski top
• Integrable quadratic Hamiltonians on so(4) and so(3,1)
• Classification of integrable quadratic Hamiltonians on e(3)
• Commutative Poisson subalgebras for the Sklyanin bracket and deformations of known integrable models
• Deformations of the Poisson brackets and the Kowalevski top
• Classical R-matrices for generalized so(p,q) tops