On the motion of a magnetized rigid body

Abstract

A method introduced by Yehia (J Phys A Math Gen 32:7565–7580, 1999 , for example) for generalizing known results of the problem of the motion of a rigid body is extended here to take magnetization by rotation (Barnett–London effect) into account. In the general case of anisotropic ferromagnets, the equations of motion are proved to be covariant under a one-parameter family of transformations which generalize the problem by inserting a parameter, with a definite physical meaning, into the dynamical equations. As an example, we generalize a particular solution of the problem of the motion of a gyrostat in a central field of attraction. It turns out that the generalized solution represents a new particular solution of the problem of the motion by inertia of a rigid body in an ideal incompressible fluid.