Geodesic
On the motion of a multidimensional body with fixed point in a gravitational field
Sbornik. Mathematics, Tome 42 (1982) no. 3, pp. 413-418 
A. V. Belyaev. On the motion of a multidimensional body with fixed point in a gravitational field. Sbornik. Mathematics, Tome 42 (1982) no. 3, pp. 413-418. http://geodesic.mathdoc.fr/item/SM_1982_42_3_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of the motion of an $n$-dimensional solid body with a fixed point in a gravitational field is considered. More precisely, the integrable case of such motion determined by certain symmetry conditions of the body is considered. These conditions are obtained as a generalization of the conditions for the Lagrange case of the motion of a three-dimensional heavy gyroscope. For the $n$-dimensional Lagrange case the collection of first integrals presented in the paper is sufficient for complete integrability. The fact that the case considered provides an example of a completely integrable Hamiltonian system with a noncommutative algebra of first integrals is of interest. Bibliography: 7 titles.

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

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[5] Bocharov A. V., “Dopolnenie k state: Struktura gamiltonovoi mekhaniki”, Uspekhi matem. nauk, XXXII:4(196) (1977), 237–240

[6] Mischenko A. S., Fomenko A. T., “Obobschennyi metod Luivillya integrirovaniya gamiltonovykh sistem”, Funkts. analiz, XII:2 (1977), 46–56

[7] Rais Mustapha, “L'indice des produits semi-directs $E \underset{\rho}{\times} g$”, serie A, C. r. Acad. Sci., 287:4 (1978), 195–197 | MR | Zbl