Dynamics of a rigid body with n ellipsoidal cavities filled with a magnetic fluid
Abstract
Equations of rotation are derived for a rigid body with n ellipsoidal cavities filled with a magnetic fluid in homogeneous vortical motion. It is shown that these equations are special cases of the Euler equations on Lie algebra of group G = SO(3) X E3 X ... X E3 (n factors of E3). A three-parameter family of integrable cases of the dynamics of a rigid body with two ellipsoidal cavities filled with an ideal incompressible fluid is indicated. These integrable cases are closely connected in the algebraic respect with the classical integrable cases of Kovalevskaia and Chaplygin.
- Publication:
-
Akademiia Nauk SSSR Doklady
- Pub Date:
- 1983
- Bibcode:
- 1983DoSSR.272.1364B
- Keywords:
-
- Cavities;
- Euler Equations Of Motion;
- Ferrofluids;
- Fluid Filled Shells;
- Rigid Structures;
- Rotating Bodies;
- Ellipsoids;
- Ideal Fluids;
- Incompressible Fluids;
- Lie Groups;
- Magnetic Properties;
- Vortices;
- Physics (General)