The stability of permanent rotations of a top with a cavity filled with liquid on a plane with friction

✍ Scribed by A.V. Karapetyan; O.V. Prokomina

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 342 KB
• Volume: 64
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(00)00028-9

✦ Synopsis

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 .,;hown 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 i:~ investigated using a modified Routh theorem [1,2]. Special cases of a spherical cavity and a weightless envelope are considered.