  Equations of motion of a charged symmetrical body in external constant and
homogeneous electric and magnetic fields are deduced starting from the
variational problem, where the body is considered as a system of charged point
particles subject to holonomic constraints. The final equations are written for
the center-of mass-coordinate, rotation matrix and angular velocity. General
solution to the equations of motion is obtained for the case of a charged ball.
For the case of a symmetrical charged body (solenoid), the task of obtaining
the general solution is reduced to the problem of a one-dimensional cubic
pseudo-oscillator. Besides, we present a one-parametric family of solutions to
the problem in elementary functions.
