Evolution of motion of a solid with a fixed point and a viscous fluid filling / E. Yu. Baranova, V. G. Vil'ke. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2013. № 1. P. 44-50 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

The inertial motion of a system consisting of a solid with a fixed point and a viscous incompressible liquid filling a spherical or ellipsoidal cavity inside the body is considered. The principal moments of inertia of the system about a fixed point are approximately equal to the principal moments of inertia of an axisymmetric body. The Reynolds number being inversely proportional to the viscosity of the liquid is assumed to be small. For the description of motion, the generalized canonical variables of Аndoyer, the motion separation method, and the averaging method are used. It is shown that the motion of the system tends to the steady rotation about the axis of the greatest moment of inertia directed along the constant angular momentum vector of the system.

Key words: solid body with a fixed point and a cavity filled with a viscous liquid, motion separation method, asymptotic method.

№ 1/2013