The stability of permanent rotations of a top with a cavity filled with liquid on a plane with frictionстатья
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Дата последнего поиска статьи во внешних источниках: 14 декабря 2016 г.
Аннотация:The problem of the motion of a heavy dynamically symmetrical sphere along a horizontal plane with friction is considered. Inside the sphere there is an axisymmetric ellipsoidal cavity, completely filled with an ideal incompressible fluid, which performs uniform rotational motion. It is shown that the system, in addition to an integral of the constancy of vortex intensity, allows of a Jellet type integral. In addition, the total mechanical energy of the system is a non-increasing function. The stability of permanent rotations of the system is investigated using a modified Routh theorem [1,2]. Special cases of a spherical cavity and a weightless envelope are considered.