Igor Komarov

ul. Ulyanovskaya 1, Petrodvorets, 198904, St. Petersburg, Russia
V.A.Fock Institute of Physics, St. Petersburg State University, Petrodvorets, St. Petersburg, Russia


Komarov I. V., Tsiganov A. V.
For the Kowalevski gyrostat change of variables similar to that of the Kowalevski top is done. We establish one to one correspondence between the Kowalevski gyrostat and the Clebsch system and demonstrate that Kowalevski variables for the gyrostat practically coincide with elliptic coordinates on sphere for the Clebsch case. Equivalence of considered integrable systems allows to construct two Lax matrices for the gyrostat using known rational and elliptic Lax matrices for the Clebsch model. Associated with these matrices solutions of the Clebsch system and, therefore, of the Kowalevski gyrostat problem are discussed. The K├Âtter solution of the Clebsch system in modern notation is presented in detail.
Citation: Komarov I. V., Tsiganov A. V.,  On integration of the Kowalevski gyrostat and the Clebsch problems, Regular and Chaotic Dynamics, 2004, vol. 9, no. 2, pp. 169-187

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