@article{SM_2008_199_6_a3,
author = {M. Yu. Ivochkin},
title = {Topological analysis of the motion of an ellipsoid on a~smooth plane},
journal = {Sbornik. Mathematics},
pages = {871--890},
year = {2008},
volume = {199},
number = {6},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2008_199_6_a3/}
}
M. Yu. Ivochkin. Topological analysis of the motion of an ellipsoid on a smooth plane. Sbornik. Mathematics, Tome 199 (2008) no. 6, pp. 871-890. http://geodesic.mathdoc.fr/item/SM_2008_199_6_a3/
[1] A. A. Burov, A. V. Karapetyan, “On the non-existence of the additional integral in the problem of the motion of a heavy rigid ellipsoid along a smooth plane”, J. Appl. Math. Mech., 49:3 (1985), 387–389 | DOI | MR | Zbl
[2] S. Smale, “Topology and mechanics. I”, Invent. Math., 10:4 (1970), 305–331 ; “Topology and mechanics. II. The planar $n$-body problem”, Invent. Math., 11:1 (1970), 45–64 | DOI | DOI | MR | MR | MR | Zbl | Zbl | Zbl
[3] A. V. Bolsinov, A. T. Fomenko, Integrable Hamiltonian systems. Geometry, topology, classification, Chapman Hall, CRC, Boca Raton, FL, 2004 | MR | MR | Zbl | Zbl
[4] A. T. Fomenko, Kh. Tsishang, “A topological invariant and a criterion for the equivalence of integrable Hamiltonian systems with two degrees of freedom”, Math. USSR-Izv., 36:3 (1991), 567–596 | DOI | MR | Zbl | Zbl
[5] A. A. Oshemkov, “Vychislenie invariantov Fomenko dlya osnovnykh integriruemykh sluchaev dinamiki tverdogo tela”, Tr. sem. po vektornomu i tenzornomu analizu, 1993, no. 25, 23–109 | Zbl
[6] Ya. V. Tatarinov, “Chastotnaya nevyrozhdennost volchka Lagranzha i uravnoveshennogo giroskopa v kardanovom podvese”, Mekhanika tverdogo tela, 1987, no. 4, 30–36
[7] S. P. Novikov, “The Hamiltonian formalism and a many-valued analogue of Morse theory”, Russian Math. Surveys, 37:5 (1982), 1–56 | DOI | MR | Zbl
[8] V. I. Arnold, A. N. Varchenko, S. M. Gusein-Zade, Osobennosti differentsiruemykh otobrazhenii, 2-e izd., MTsNMO, M., 2004 ; ; V. I. Arnol'd, S. M. Gusejn-Zade, A. N. Varchenko, Singularities of differentiable maps, vol. I, Monogr. Math., 82, Birkhäuzer, Boston, MA, 1985 ; Singularities of differentiable maps, vol. II, Monogr. Math., 83, Birkhäuzer, Boston, MA, 1988 | MR | Zbl | MR | MR | Zbl | MR | Zbl
[9] J. W. Bruce, P. J. Giblin, Curves and singularities. A geometrical introduction to singularity theory, Cambridge Univ. Press, Cambridge, 1984 | MR | MR | Zbl | Zbl