that without the balancing system it would topple over. A spinning wheel is mounted in a gimbal frame whose axis of rotation (the precession axis) is perpendicular to the spin axis. The assembly is mounted on the vehicle chassis such that, at equilibrium, the spin axis, precession axis and vehicle roll axis are mutually perpendicular. Forcing the gimbal to rotate causes the wheel to precess resulting in gyroscopic torques about the roll axis, so that the mechanism has the potential to right the vehicle when tilted from the vertical. The wheel shows a tendency to align its spin axis with the axis of rotation (the gimbal axis), and it is this action which rotates the entire vehicle about its roll axis. Ideally, the mechanism applying control torques to the gimbal ought to be passive (an arrangement of springs, dampers and levers), but the fundamental nature of the problem indicates that this would be impossible. The equilibrium position is with the vehicle upright, so that any disturbance from this position reduces the height of the centre of gravity, lowering the potential energy of the system. Whatever returns the vehicle to equilibrium must be capable of restoring this potential energy, and hence cannot consist of passive elements alone. The system must contain an active servo of some kind. Side loads If constant side forces were resisted by gyroscopic action alone, the gimbal would rotate quickly on to the stops, and the vehicle would topple. In fact, the mechanism causes the vehicle to lean into the disturbance, resisting it with a component of weight, with the gyro near its undeflected position. Inertial side forces, arising from cornering, cause the vehicle to lean into the corner. A single gyro introduces an asymmetry which will cause the vehicle to lean too far, or not far enough for the net force to remain in the plane of symmetry, so side forces will still be experienced on board. In order to ensure that the vehicle banks correctly on corners, it is necessary to remove the gyroscopic torque arising from the vehicle rate of turn. A free gyro keeps its orientation with respect to inertial space, and gyroscopic moments are generated by rotating it about an axis perpendicular to the spin axis. But the control system deflects the gyro with respect to the chassis, and not with respect to the fixed stars. It follows that the pitch and