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An \(L\)-\(A\) pair for the Hess-Apel’rot system and a new integrable case for the Euler-Poisson equations on \(so(4)\times so(4)\). (English) Zbl 1010.70004
Summary: We present an L-A pair for the Hess-Apel’rot case of a heavy rigid three-dimensional body. Using it, we give an algebro-geometric integration procedure which leads to a new completely integrable case of Euler-Poisson equations in dimension four. Explicit formula are given for integrals in involution. This system is a counterexample to one of Ratiu’s theorems [T. Ratiu, Am. J. Math. 104, 409-448 (1982; Zbl 0509.58026)]. A corrected version of this classification theorem is proved.

MSC:
70E17 Motion of a rigid body with a fixed point
70E40 Integrable cases of motion in rigid body dynamics
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