On Optimal Rigid Body Rotation with Internal Forces Application

The article describes the result obtained for the problem of a rigid body’s maximum rotation in a given time interval by moving a movable internal mass. The mass movement is achieved by applying limited force. Previously, similar problems were considered in which the displacements of internal mass were assumed to be kinematic with restrictions on the point’s speed. The obtained result is described by analytical, easily verifiable formulas. The optimal trajectory of the moving mass is a spiral that coils around the center of mass of a rigid body with a frequency increasing to infinity. The obtained numerical results relate to the design of other optimal trajectories that cannot be analyzed analytically.