Optimal control of the pumping and damping of a swing

Abstract The problem of controlling, maximizing or minimizing the inclination of a swing to the vertical at its highest point is considered. The swing is modelled by a plane compound pendulum on which a point mass is located. This point can be displaced within limits along the straight line passing through the axis of support of the pendulum and its centre of mass. Viscous and dry friction are taken into account at the supporting axis, together with “aerodynamic” drag that is linear in the velocity and acting on the moving point. The controlling variable is the distance from the axis of support to the moveable point.