New integrable cases in the dynamics of rigid bodies. IV (Q1119033)

In the present paper a new general integrable case of motion of a rigid body about a fixed point is introduced. The body is assumed to have complete dynamical symmetry at the fixed point. Unlike all the cases considered in our previous articles [parts I-III, the author, ibid. 13, 169-172 (1986; Zbl 0606.70008); 14, 51-56 (1987; Zbl 0621.70002) and 14, 177-180 (1987; Zbl 0635.70006)], the motion occurs under the action of certain potential and gyroscopic forces which admit an axis of symmetry fixed in the body but no such axis in space. A physical interpretation of this case is given.