Invariant Relations For Kirchhoff Equations And The Kowalewski Method

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Integrable Euler Equations on SO (4) and their Physical

for these equations; they were found by Steklov [1], Lyapunov [2], Kowalewski [3], and Chaplygin [4]. According to Liouville, it is sufficient to find an additional first integral J 4 to make sure that the Hamiltonian system (1.3) [or the system (1.4)] on the orbits & is integrable. The method which is used in the present work to construct the

Integrable Hamiltonian Systems on Lie Groups: Kowalewski Type

Kowalewski's method of integration extends to the elastic problem with only minor modifications and leads to hyperelliptic differential equations on Abelian varieties on the Lie algebra of G. Faced with the mysterious change of vari-ables in Kowalewski's paper, whose mathematical nature was never properly