关于多维刚体相对平衡的一点注记
A note on relative equilibria of multidimensional rigid body
摘要：
众所周知，自由通用三维刚体的旋转是静止的，当且仅当它是围绕三个惯性主轴之一的旋转。正如许多作者所指出的那样，类似的结果对于多维物体也是正确的：旋转是静止的当且仅当它是在惯性主轴上的旋转，只要角速度矩阵的特征值是两两不同的。然而，如果静止旋转的角速度矩阵的某些特征值重合，则该旋转可能具有不同的性质。本文给出了这种旋转的描述。
英文摘要：
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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