Geodesic
Euler equations on finite-dimensional solvable Lie groups
Izvestiya. Mathematics , Tome 17 (1981) no. 2, pp. 405-412

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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. 
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     author = {V. V. Trofimov},
     title = {Euler equations on finite-dimensional solvable {Lie} groups},
     journal = {Izvestiya. Mathematics },
     pages = {405--412},
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     volume = {17},
     number = {2},
     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1981_17_2_a8/}
}
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V. V. Trofimov. Euler equations on finite-dimensional solvable Lie groups. Izvestiya. Mathematics , Tome 17 (1981) no. 2, pp. 405-412. http://geodesic.mathdoc.fr/item/IM2_1981_17_2_a8/