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Euler equations on finite-dimensional solvable Lie groups

V. V. Trofimov


Abstract: In this paper a construction of “rigid body” operators on Borel subalgebras is given. Complete integrability of Euler equations with such operators is proved. In addition, using a noncommutative method of integrating Hamiltonian systems, complete integrability of an “unconstrained rigid body” on the cotangent bundle of a Borel subgroup is proved.
Bibliography: 10 titles.

UDC: 513.944

MSC: Primary 58F07; Secondary 58F05, 70H05, 22E25

Received: 14.09.1979

 English version: Mathematics of the USSR-Izvestiya, 1981, 17:2, 405–412

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