The stability of the steady motion of a gyrostat with a liquid in a cavity

✍ Scribed by T.V. Rudenko

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 565 KB
• Volume: 66
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(02)00022-9

✦ Synopsis

A symmetrical rigid body with a spherical base, carrying a rotor and having a cavity in the shape of an ellipsoid of revolution, completely filled with an ideal incompressible liquid in uniform vortex motion, is moving along an absolutely rough plane. It is shown that this system admits of an energy integral, Jellett's integral, the integral of constant vorticity and a geometric integral. The construction of a Lyapunov function as a linear combination of first integrals [l] yields the sufficient conditions for the rotation of the gyrostat about the vertically positioned axis of symmetry to be stable. The conditions for the gyrostat's rotation to be unstable are found. It is shown that the rotor may prove to have either a stabilizing or destabilizing effect on the system and that the gyrostat admits of motions of the type of regular precession. The sufficient conditions for the stability of these motions are obtained.