Note on Free Symmetric Rigid Body Motion

作者：Dragovic Vladimir^*; Gajic Borislav; Jovanovic Bozidar

来源：Regular & Chaotic Dynamics, 2015, 20(3): 293-308.

DOI：10.1134/S1560354715030065

• Euler equations
• Manakov integrals
• spectral curve
• reduced Poisson space

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.

• 出版日期2015-5