On optimal rotation of a rigid body by applying internal forces

The article describes results obtained for the problem of maximum rotation of a rigid body in a given time interval by moving an internal mass. The mass moves by applying a bounded force. Previously, similar problems were considered in which the displacements of an internal mass point were assumed to be kinematic with constrains imposed on the point’s speed. The obtained results are described by analytical, easily verifiable formulas. The optimal trajectory of the moving mass is a spiral that coils around the center of mass of the rigid body with a frequency increasing to infinity.