New integrable problems of motion of a rigid body acted upon by nonsymmetric electromagnetic forces

The problem of motion of a rigid body with a spherical dynamical symmetry about a fixed point under the action of a combination of nonsymmetric nonuniform electric, magnetic, gravitational and Lorentz forces is considered. Two systems of equations of motion written in the body system and in the inertial system are shown to have the same structure. Transforming some recently found integrable cases of a nonsymmetric body in an axial combination of fields, we construct two new integrable cases of a body in a nonsymmetric combination of fields. In the latter cases, the body is assumed to have distributions of electric charges, mass and magnetization which exhibit a common axis of symmetry and carries a rotor along that axis. Explicit solution of the equations of motion is discussed.