On the motion of a~multidimensional body with fixed point in a~gravitational field
Sbornik. Mathematics, Tome 42 (1982) no. 3, pp. 413-418
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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.
@article{SM_1982_42_3_a7,
author = {A. V. Belyaev},
title = {On the motion of a~multidimensional body with fixed point in a~gravitational field},
journal = {Sbornik. Mathematics},
pages = {413--418},
publisher = {mathdoc},
volume = {42},
number = {3},
year = {1982},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1982_42_3_a7/}
}
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/