Note on Free Symmetric Rigid Body Motion

    2015, Volume 20, Number 3, pp.  293-308

    Author(s): Dragović V., Gajić B., Jovanović B.

    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
    Citation: Dragović V., Gajić B., Jovanović B., Note on Free Symmetric Rigid Body Motion, Regular and Chaotic Dynamics, 2015, Volume 20, Number 3, pp. 293-308

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