A note on relative equilibria of multidimensional rigid body
Mathematical Physics
2012-09-27 v1 math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1202.4082,
title = {A note on relative equilibria of multidimensional rigid body},
author = {Anton Izosimov},
journal= {arXiv preprint arXiv:1202.4082},
year = {2012}
}