On the regular precession of an asymmetric rigid body acted upon by uniform gravity and magnetic fields

In 1947 Grioli discovered that an asymmetric heavy rigid body moving about a fixed point can perform a regular precession, which is the rotation of the body about an axis fixed in it,while that axis precesses with the same uniform angular velocity about a non-vertical axis fixed in space.In the present note, we show that a magnetized asymmetric rigid body moving about a fixed point while acted upon by uniform gravity and magnetic fields can perform a regular precession about a horizontal axis fixed in space orthogonal to the magnetic field. This motion does not contain Grioli s as a special case since the gravity and magnetic effects are coupled and can vanish only simultaneously.