Stabilisation and motion control of unstable objects A pendulum with stationary pivot A pendulum with wheel based pivot A pendulum with a flywheel Wheel rolling control by means of a pendulum Optimal swinging and damping of a swing Pendulum control that minimizes energy consumption Local stabilization of an inverted pendulum by means of a single control torque Optimal control design for swinging and damping a double pendulum Global stabilization of an inverted pendulum controlled by torque in the inter link jointinverted pendulum Global stabilization of an inverted pendulum controlled by torque in the pivot Multi link pendulum on a moving base Stabilization of a ball on a straight beam Stabilization of a ball on a curvilinear beam Bicycle design Designing a control law to stabilize the bicycle tilt Bang bang control and fluent control Trapezoidal control for a system with compliant elements Systems with mechanical degrees of freedom containing unstable objects are analysed in this monograph and algorithms for their control are developed discussed and numerically tested. This is achieved by identifying unstable modes of motion and using all available resources to suppress them. By using this approach the region of states from which a stable regime can be reached is maximised. The systems discussed in this book are models for pendula and vehicles and find applications in mechatronics robotics as well as in mechanical and automotive engineering