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.
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
\Bibitem{Kha14}
\by Mikhail~P.~Kharlamov
\paper Extensions of the Appelrot Classes for the Generalized
Gyrostat in a Double Force Field
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 2
\pages 226--244
\mathnet{http://mi.mathnet.ru/rcd128}
\crossref{https://doi.org/10.1134/S1560354714020063}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3189259}
\zmath{https://zbmath.org/?q=an:1309.70007}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000334198000006}
Linking options:
https://www.mathnet.ru/eng/rcd128
https://www.mathnet.ru/eng/rcd/v19/i2/p226
This publication is cited in the following 7 articles:
P. E. Ryabov, S. V. Sokolov, “Phase Topology of Two Vortices of Identical Intensities in a Bose – Einstein Condensate”, Rus. J. Nonlin. Dyn., 15:1 (2019), 59–66
P. E. Ryabov, “Bifurcations of Liouville tori in a system of two vortices of positive intensity in a Bose–Einstein condensate”, Dokl. Math., 99:2 (2019), 225–229
Mikhail P. Kharlamov, Pavel E. Ryabov, Alexander Yu. Savushkin, “Topological Atlas of the Kowalevski–Sokolov Top”, Regul. Chaotic Dyn., 21:1 (2016), 24–65
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Generalizations of the Kovalevskaya case and quaternions”, Proc. Steklov Inst. Math., 295 (2016), 33–44
M. P. Kharlamov, P. E. Ryabov, I. I. Kharlamova, “Topological Atlas of the Kovalevskaya–Yehia Gyrostat”, J. Math. Sci. (N. Y.), 227:3 (2017), 241–386
P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317
P. E. Ryabov, “New invariant relations for the generalized two-field gyrostat”, J. Geom. Phys., 87 (2015), 415–421
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