A note on relative equilibria of a free multidimensional rigid bodyстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация: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 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 fixing planes spanned by 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 this paper.