Аннотация:
The Poincaré – Zhukovsky – Hough model describing the motion of a rigid body with an
ellipsoidal cavity filled with an ideal vortex liquid is used. The possibility of regular precession
in a uniform force field of a system not possessing axial symmetry is shown. For the case where
the axis of proper rotation is one of the system principal inertia axes and the center of gravity
lies on this axis, two conditions of precession are obtained. One of the conditions coincides with
the condition of regular precession in the absence of external forces for the system without axial
symmetry found earlier by the author. This condition imposes one constraint on the system
configuration. The other condition relates the proper rotation and precession velocities to the
mechanical parameters of the system. A record is given of the conditions in the form of relations
between the inertia moments of the rigid shell and the semiaxes of the ellipsoidal cavity, as well
as between the distance to the center of gravity and the nutation angle, the precession velocity
and the proper rotation velocity. It is shown that in the case where the cavity differs little from
the sphere, the conditions obtained differ from the Lagrange conditions for an axisymmetric
rigid body with a fixed point in a uniform gravity field by small values of the second order.
Ключевые слова:
rigid body with liquid filling, Poincaré – Zhukovsky – Hough equations, uniform force field, regular precession, system without axial symmetry
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