A. Kostko

198904, St.-Petersburg, Petrodvorec, Ulyanovskaya str.,1
St.-Petersburg State University, Institute of science-research of Physics


Kostko A. L., Tsiganov A. V.
The bi-hamiltonian structures for the Goryachev–Chaplygin top are constructed by using the Chaplygin variables and the Sklyanin bracket.
Keywords: integrable and bi-hamiltonian system, the Goryachev–Chaplygin top
Citation: Kostko A. L., Tsiganov A. V.,  On the Bi-Hamiltonian Structures for the Goryachev–Chaplygin Top, Regular and Chaotic Dynamics, 2008, vol. 13, no. 1, pp. 37-44
Kostko A. L., Tsiganov A. V.
Noncanonical transformations of the spherical top
2003, vol. 8, no. 2, pp.  143-154
We discuss noncanonical transformations connecting different integrable systems on the symplectic leaves of the Poisson manifolds. The special class of transformations, which consists of the symplectic mappings of symplectic leaves and of the parallel transports induced by diffeomorphisms in the base of symplectic foliation, is considered. As an example, we list integrable systems associated with the spherical top. The corresponding additional integrals of motion are second, third and six order polynomials in momenta.
Citation: Kostko A. L., Tsiganov A. V.,  Noncanonical transformations of the spherical top, Regular and Chaotic Dynamics, 2003, vol. 8, no. 2, pp. 143-154

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