Kharlamov M.P., Savushkin A.Yu. Geometrical approach to the separation of variables in mechanical systems

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Khramov Sergei Vladimirovich
 
Postgraduate student, Department of Radiophysics, Volgograd State University
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Ulitca Gagarina, 8, 400131 Volgograd, Russian Federation
 
Savushkin Alexander Yurievich
 
andidate of Physics and Mathematics, Associate Professor, Department of Computer Systems and Mathematical Simulation, Volgograd Academy of Public Administration
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Ulitca Gagarina, 8, 400131 Volgograd, Russian Federation
 
Abstract. The article presents the analytical results received with the help of computer aided symbolic calculations in the problem of motion of the rigid body in two constant fields. The Liouville integrability of this system under certain condition of the Kowalevski type was established by A.G.Reyman and M.A.Semenov-Tian-Shansky. We consider the geometrical basis for obtaining a separation of variables. Two systems of local planar coordinates are introduced in which the projections of integral manifolds of the critical subsystems become rectangular. The separated equations are obtained for two subsystems with the help of Mathematica 7.
 
Key words: integrable system, rigid body dynamics, double force field, separation of variables.

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Geometrical approach to the separation of variables in mechanical systems by Kharlamov M.P., Savushkin A.Yu. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. Issue 13 2010 pp. 47-74
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