Аннотация:
It is proven that the completely integrable general Kirchhoff case of the Kirchhoff equations for B≠0 is not an algebraic complete integrable system. Similar analytic behavior of the general solution of the Chaplygin case is detected. Four-dimensional analogues of the Kirchhoff and the Chaplygin cases are defined on e(4) with the standard Lie–Poisson bracket.
The research was partially supported by the Serbian Ministry of Education and Science, Project 174020 Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems and by the Mathematical Physics Group of the University of Lisbon, Project Probabilistic approach to finite and infinite dimensional dynamical systems, PTDC/MAT/104173/2008.
Поступила в редакцию: 13.10.2011 Принята в печать: 11.04.2012
Образец цитирования:
Vladimir Dragović, Borislav Gajić, “On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations”, Regul. Chaotic Dyn., 17:5 (2012), 431–438
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\by Vladimir Dragovi\'c, Borislav Gaji\'c
\paper On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 5
\pages 431--438
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\crossref{https://doi.org/10.1134/S156035471205005X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2989515}
\zmath{https://zbmath.org/?q=an:1252.70022}
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd413
https://www.mathnet.ru/rus/rcd/v17/i5/p431
Эта публикация цитируется в следующих 5 статьяx:
Essmann E., Shui P., Popinet S., Zaleski S., Valluri P., Govindarajan R., “Chaotic Orbits of Tumbling Ellipsoids”, J. Fluid Mech., 903 (2020), A10
Pantelis A. Damianou, “Poisson Brackets after Jacobi and Plücker”, Regul. Chaotic Dyn., 23:6 (2018), 720–734
Alina Dobrogowska, Grzegorz Jakimowicz, “Tangent lifts of bi-Hamiltonian structures”, Journal of Mathematical Physics, 58:8 (2017)
Vladimir Dragović, Borislav Gajić, “Some Recent Generalizations of the Classical Rigid Body Systems”, Arnold Math J., 2:4 (2016), 511
Alina Dobrogowska, Tomasz Goliński, “Lie bundle on the space of deformed skew-symmetric matrices”, Journal of Mathematical Physics, 55:11 (2014)
Цитирование в формате AMSBIB
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