A note on relative equilibria of multidimensional rigid body

Details A note on relative equilibria of multidimensional rigid body A note on relative equilibria of multidimensional rigid body

2012-02-18

arxiv.org/abs/1202.4082v1

Physics

Mathematical Physics

Scientific paper

It is well known that a rotation of a free generic three-dimensional rigid body is stationary if and only if it is a rotation around one of three principal axes of inertia. As it was noted by many authors, the analogous result is true for a multidimensional body: a rotation is stationary if and only if it is a rotation in the principal axes of inertia, provided that the eigenvalues of the angular velocity matrix are pairwise distinct. However, if some eigenvalues of the angular velocity matrix of a stationary rotation coincide, then it is possible that this rotation has a different nature. A description of such rotations is given in the present paper.

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