Control of motion of an inhomogeneous cylinder with internal movable masses along a horizontal plane

The controlled motion of a rigid inhomogeneous cylinder over a rough horizontal plane is considered. The control is provided by controlled motion of internal masses. Mathematical models are constructed that correspond to rolling without loss of contact or slippage. The conditions for the physical implementability of such a motion are derived. The case where the internal moving masses from a rigid flywheel the centre of inertia of which lies on the axis of the cylinder is investigated in detail. A near-time-optimal feedback control that enables the total energy to be changed in a required way is constructed on the basis of an asymptotic approach. The main operating modes are simulated, namely, swinging up of the cylinder to a large angular amplitude, rotation with a prescribed energy, deceleration of rolling to a complete stop, and oscillations and rotations in the neighbourhood of the separatrix.