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This article is cited in 7 scientific papers (total in 7 papers)
Extensions of the Appelrot Classes for the Generalized
Gyrostat in a Double Force Field
Mikhail P. Kharlamov Russian Academy of National Economy and Public Administration, Volgograd branch,
ul. Gagarina 8, Volgograd, 400131 Russia
Abstract:
For the integrable system on $e(3,2)$ found by Sokolov and Tsiganov we
obtain explicit equations of some invariant 4-dimensional manifolds on
which the induced systems are almost everywhere Hamiltonian with two
degrees of freedom. These subsystems generalize the famous Appelrot
classes of critical motions of the Kowalevski top. For each subsystem we
point out a commutative pair of independent integrals, describe the sets
of degeneration of the induced symplectic structure. With the help of the
obtained invariant relations, for each subsystem we calculate the outer
type of its points considered as critical points of the initial system
with three degrees of freedom.
Keywords:
generalized two-field gyrostat, critical subsystems, Appelrot classes, invariant relations, types of critical points.
Received: 05.09.2013 Accepted: 30.10.2013
Citation:
Mikhail P. Kharlamov, “Extensions of the Appelrot Classes for the Generalized
Gyrostat in a Double Force Field”, Regul. Chaotic Dyn., 19:2 (2014), 226–244
Linking options:
https://www.mathnet.ru/eng/rcd128 https://www.mathnet.ru/eng/rcd/v19/i2/p226
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