To describe the rotation of a rigid body with an ellipsoidal cavity filled with an ideal vorticated liquid, the Poincare–Hough–Zhukovsky equations are used. It is obtained constraints (hereinafter referred to as configuration conditions) on the mass distribution and cavity dimensions of an asymmetric liquid-filled rigid body under which the rigid body can perform the regular precession. Two possible nontrivial cases are indicated when one or two components of the direct vector of the axis of proper rotation are equal to zero. It is shown that if the axis of proper rotation coincides with one of the principal axes of inertia of the system, it suffices to fulfill one configuration condition. The ratio between the periods of proper rotation and precession is found. The regular precession of a system in which the principal moments of inertia are close to each other and the cavity is close to spherical is considered. For the case when the difference between the two equatorial moments of inertia is an order of magnitude smaller than the difference between the equatorial and polar moments, the main part of the ratio between the periods coincides with the Euler period, and the correction is due to the inequality between the equatorial moments of inertia. In the case when the axis of proper rotation is orthogonal to a principal axis and is not coincident with any other principal axis, the number of configuration conditions is two. Expressions for the rates of precession and proper rotation are obtained, and the position in the body of the axis of proper rotation is indicated. Special cases are given that allow simplification of the configuration conditions.

中文翻译：

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非对称充液刚体规则进动的新案例

为了描述一个刚体的旋转，该刚体的椭圆腔充满了理想的涡流液体，可以使用 Poincare-Hough-Zhukovsky 方程。得到了非对称充液刚体的质量分布和空腔尺寸的约束条件（以下简称构型条件），在该条件下刚体可以进行规则进动。当正确旋转轴的直接矢量的一个或两个分量为零时，表示了两种可能的非平凡情况。结果表明，如果适当的旋转轴与系统的惯性主轴之一重合，则足以满足一种配置条件。找到适当旋转和岁差的周期之间的比率。考虑系统的规则进动，其中主惯性矩彼此接近且腔体接近球形。对于两个赤道转动惯量之差比赤道和极矩之差小一个数量级的情况，周期比的主要部分与欧拉周期重合，修正是由于赤道转动惯量之间的不等式。在适当旋转的轴与主轴正交且不与任何其他主轴重合的情况下，配置条件的数量为两个。得到了进动率和正转率的表达式，并指出了正转轴在体中的位置。