ABSTRACT In this paper, the integrability of the equations of a system of three vortex sources is... more ABSTRACT In this paper, the integrability of the equations of a system of three vortex sources is shown. A reduced system describing, up to similarity, the evolution of the system’s configurations is obtained. Possible phase portraits and various relative equilibria of the system are presented.
Generalizations of the Kovalevskaya, Chaplygin, Goryachev-Chaplygin and Bogoyavlensky systems on ... more Generalizations of the Kovalevskaya, Chaplygin, Goryachev-Chaplygin and Bogoyavlensky systems on a bundle are considered in this paper. More- over, a method of introduction of separating variables and action-angle vari- ables is described. Another integration method for the Kovalevskaya top on the bundle is found. This method uses a coordinate transformation that re- duces the Kovalevskaya system to the Neumann system.
ABSTRACT In this paper, the integrability of the equations of a system of three vortex sources is... more ABSTRACT In this paper, the integrability of the equations of a system of three vortex sources is shown. A reduced system describing, up to similarity, the evolution of the system’s configurations is obtained. Possible phase portraits and various relative equilibria of the system are presented.
Generalizations of the Kovalevskaya, Chaplygin, Goryachev-Chaplygin and Bogoyavlensky systems on ... more Generalizations of the Kovalevskaya, Chaplygin, Goryachev-Chaplygin and Bogoyavlensky systems on a bundle are considered in this paper. More- over, a method of introduction of separating variables and action-angle vari- ables is described. Another integration method for the Kovalevskaya top on the bundle is found. This method uses a coordinate transformation that re- duces the Kovalevskaya system to the Neumann system.
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Papers by I. Mamaev