Dynamics of solid body with ellipsoidal cavity containing magnetic fluid

The motion of a perfectly solid body with an ellipsoidal cavity containing a magnetic fluid was analyzed. The motion of this body is described by the MHD equations and the law of conservation of total angular momentum. The problem of dynamics is solved with the classical approach of considering a time interval sufficiently short for the effects of fluid viscosity and of fluid friction against the cavity wall to be negligible. The resolvent system of three equations, obtained after transformation from Lagrange to Euler coordinates, generalizes the classical equations of motion for a body with an ellipsoidal cavity containing an ideal fluid. The most important integral is that of total energy, the sum of kinetic energy of the fluid + internal energy of the magnetic field + kinetic energy of the body rotation. In the case of zero total angular momentum these equations become analogous to the classical Kirchhoff equations of motion for a solid body with three planes of symmetry in a fluid medium. A two-parametric family of values for the inertia tensor satisfying the Clebsch condition for integrability of the system of dynamics equations is shown to exist for an ellipsoid with any ratio of semiaxes.