  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.
