Abstract
The Kowalewski exponents in the problem on the motion of a solid under the Chaplygin condition are calculated (when there is a velocity-linear invariant relation). The method of calculation uses the generalizing Ioshida theorems on the Kowalewski exponents found by V.V. Kozlov. It is shown that the general solution of the equations of motion branches out in the complex time plane under the Chaplygin conditions.
Similar content being viewed by others
References
G. Kirchhoff, Mechanics (Izd-vo AN SSSR, Moscow, 1962) [in Russian].
H. Yoshida, Celestial Mech. 31, 363 (1983).
V. V. Kozlov, Mat. Zametki 51 (2), 46 (1992).
V. V. Kozlov, Dokl. Akad. Nauk 249 (6), 1299 (1979).
V. V. Kozlov and D. A. Onishchenko, Dokl. Akad. Nauk 266 (6), 1298 (1982).
V. V. Kozlov, Symmetry, Topology, and Resonances in Hamiltonian Mechanics (Udmurt. Un-t, Izhevsk, 1995).
S. L. Ziglin, Tr. MMO 41, 287 (1980).
V. V. Kozlov, Prikl. Mat. Mekh. 42 (3), 400 (1978).
S. L. Ziglin, Funktsion. Analiz Prilozh. 16 (3), 30 (1983); 17 (1), 8 (1983).
V. V. Kozlov, Prikl. Mat. Mekh. 79 (3), 307 (2015).
A. M. Lyapunov, Soobshch. Khar’k. Mat. O-va 4 (3), 123 (1894).
S. A. Chaplygin, Mat. Sb. 20 (1), 115; 20 (2), 173 (1897).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N.V. Denisova, 2017, published in Doklady Akademii Nauk, 2017, Vol. 472, No. 1, pp. 33–35.
Rights and permissions
About this article
Cite this article
Denisova, N.V. Invariant relations for kirchhoff equations and the Kowalewski method. Dokl. Phys. 62, 24–26 (2017). https://doi.org/10.1134/S1028335817010013
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1028335817010013