Geodesic
Topological analysis of the motion of an ellipsoid on a smooth plane
Sbornik. Mathematics, Tome 199 (2008) no. 6, pp. 871-890 
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/
@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/}
}
TY  - JOUR
AU  - M. Yu. Ivochkin
TI  - Topological analysis of the motion of an ellipsoid on a smooth plane
JO  - Sbornik. Mathematics
PY  - 2008
SP  - 871
EP  - 890
VL  - 199
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/SM_2008_199_6_a3/
LA  - en
ID  - SM_2008_199_6_a3
ER  - 
%0 Journal Article
%A M. Yu. Ivochkin
%T Topological analysis of the motion of an ellipsoid on a smooth plane
%J Sbornik. Mathematics
%D 2008
%P 871-890
%V 199
%N 6
%U http://geodesic.mathdoc.fr/item/SM_2008_199_6_a3/
%G en
%F SM_2008_199_6_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of the motion of a dynamically and geometrically symmetric heavy ellipsoid on a smooth horizontal plane is investigated. The problem is integrable and can be considered a generalization of the problem of motion of a heavy rigid body with fixed point in the Lagrangian case. The Smale bifurcation diagrams are constructed. Surgeries of tori are investigated using methods developed by Fomenko and his students. Bibliography: 9 titles.

[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