Abstract:
We continue the analytical solution of the integrable system with two degrees of freedom arising as the generalization of the 4th Appelrot class of motions of the Kowalevski top for the case of two constant force fields [Kharlamov, RCD, vol. 10, no. 4]. The separated variables found in [Kharlamov, RCD, vol. 12, no. 3] are complex in the most part of the integral constants plane. Here we present the real separating variables and obtain the algebraic expressions for the initial Euler–Poisson variables. The finite algorithm of establishing the topology of regular integral manifolds is described. The article straightforwardly refers to some formulas from [Kharlamov, RCD, vol. 12, no. 3].
Keywords:
Kowalevski top, double field, Appelrot classes, separation of variables.
Citation:
M. P. Kharlamov, “Separation of variables in the generalized 4th Appelrot class. II. Real solutions”, Regul. Chaotic Dyn., 14:6 (2009), 621–634
\Bibitem{Kha09}
\by M. P. Kharlamov
\paper Separation of variables in the generalized 4th Appelrot class. II. Real solutions
\jour Regul. Chaotic Dyn.
\yr 2009
\vol 14
\issue 6
\pages 621--634
\mathnet{http://mi.mathnet.ru/rcd1003}
\crossref{https://doi.org/10.1134/S1560354709060021}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2591864}
\zmath{https://zbmath.org/?q=an:1229.70013}
Linking options:
https://www.mathnet.ru/eng/rcd1003
https://www.mathnet.ru/eng/rcd/v14/i6/p621
This publication is cited in the following 8 articles:
M. P. Kharlamov, P. E. Ryabov, “Topological atlas of the Kovalevskaya top in a double field”, J. Math. Sci., 223:6 (2017), 775–809
H.M. Yehia, “On the regular precession of an asymmetric rigid body acted upon by uniform gravity and magnetic fields”, Egyptian Journal of Basic and Applied Sciences, 2:3 (2015), 200
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
P. E. Ryabov, “Phase topology of one irreducible integrable problem in the dynamics
of a rigid body”, Theoret. and Math. Phys., 176:2 (2013), 1000–1015
P. E. Ryabov, M. P. Kharlamov, “Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field”, Sb. Math., 203:2 (2012), 257–287
M. P. Kharlamov, “Topologicheskii analiz i bulevy funktsii: II. Prilozheniya k novym algebraicheskim resheniyam”, Nelineinaya dinam., 7:1 (2011), 25–51
M. P. Kharlamov, “Topologicheskii analiz i bulevy funktsii: I. Metody i prilozheniya k klassicheskim sistemam”, Nelineinaya dinam., 6:4 (2010), 769–805
P. E. Ryabov, M. P. Kharlamov, “Analiticheskaya klassifikatsiya osobennostei obobschennogo volchka Kovalevskoi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2010, no. 2, 19–28
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