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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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/

[1] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[2] Kirillov A. A., Elementy teorii predstavlenii, Nauka, M., 1972 | MR

[3] Diksme Zh., Universalnye obertyvayuschie algebry, Mir, M., 1978 | MR

[4] Mischenko A. S., Fomenko A. T., “Uravneniya Eilera na konechnomernykh gruppakh Li”, Izv. AN SSSR. Ser. matem., 42 (1978), 396–415 | MR | Zbl

[5] Mischenko A. S., Fomenko A. T., “Obobschennyi metod Liuvillya integrirovaniya gamiltonovykh sistem”, Funkts. analiz i ego prilozheniya, 12:2 (1978), 46–56 | MR | Zbl

[6] Trofimov V. V., “Uravneniya Eilera na borelevskikh podalgebrakh poluprostykh algebr Li”, Izv. AN SSSR. Ser. matem., 43 (1979), 714–732 | MR | Zbl

[7] Arkhangelskii A. A., “Vpolne integriruemye gamiltonovy sistemy na gruppe treugolnykh matrits”, Matem. sb., 108:1 (1979), 134–142 | MR

[8] Maltsev A. I., “Kommutativnye podalgebry poluprostykh algebr Li”, Izv. AN SSSR. Ser. matem., 9 (1945), 291–300 | Zbl

[9] Marsden J., Weinstein A., “Reduction of symplectic manifolds with symmetry”, Reports on math. physics, 5:1 (1974), 121–130 | DOI | MR | Zbl

[10] Mischenko A. S., Fomenko A. T., “Integriruemost uravnenii Eilera na poluprostykh algebrakh Li”, Trudy seminara po vektornomu i tenzornomu analizu, t. XIX, 1979, 3–94 | Zbl