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Regul. Chaotic Dyn., 2015, Volume 20, Issue 3, Pages 293–308 (Mi rcd44)  

Note on Free Symmetric Rigid Body Motion

Vladimir Dragovićab, Borislav Gajića, Božidar Jovanovića

a Mathematical Institute SANU, Kneza Mihaila 36, 11000 Belgrade, Serbia
b Department of Mathematical Sciences, The University of Texas at Dallas, 800 West Campbell Road 75080 Richardson TX, USA

Abstract: We consider the Euler equations of motion of a free symmetric rigid body around a fixed point, restricted to the invariant subspace given by the zero values of the corresponding linear Noether integrals. In the case of the $SO(n-2)$-symmetry, we show that almost all trajectories are periodic and that the motion can be expressed in terms of elliptic functions. In the case of the $SO(n-3)$-symmetry, we prove the solvability of the problem by using a recent Kozlov’s result on the Euler–Jacobi–Lie theorem.

Keywords: Euler equations, Manakov integrals, spectral curve, reduced Poisson space

Funding Agency Grant Number
Ministry of Education, Science and Technical Development of Serbia 174020
The research was supported by the Serbian Ministry of Education and Science Project 174020 Geometry and Topology of Manifolds, Classical Mechanics, and Integrable Dynamical Systems.


DOI: https://doi.org/10.1134/S156035471503006

References: PDF file   HTML file

Bibliographic databases:

MSC: 37J35, 70H06, 70E45
Received: 30.04.2015
Language:

Citation: Vladimir Dragović, Borislav Gajić, Božidar Jovanović, “Note on Free Symmetric Rigid Body Motion”, Regul. Chaotic Dyn., 20:3 (2015), 293–308

Citation in format AMSBIB
\Bibitem{DraGajJov15}
\by Vladimir Dragovi\'c, Borislav Gaji\'c, Bo{\v z}idar Jovanovi\'c
\paper Note on Free Symmetric Rigid Body Motion
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 293--308
\mathnet{http://mi.mathnet.ru/rcd44}
\crossref{https://doi.org/10.1134/S156035471503006}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3357277}
\zmath{https://zbmath.org/?q=an:06488658}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015RCD....20..293D}


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