|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Note on free symmetric rigid body motion||Journal:||Regular and Chaotic Dynamics||Volume:||20||Issue:||3||First page:||293||Last page:||308||Issue Date:||19-May-2015||Rank:||M22||ISSN:||1560-3547||DOI:||10.1134/S1560354715030065||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 | reduced Poisson space | spectral curve||Publisher:||Springer Link|
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