the equations of motion in and will be
(61) |
If , then the motions in and will be independent of each other. If is also 0, then we have the relation
(62) |
and if this is fulfilled, the disturbances of the motion in will have no effect on the motion in . The teeth of the differential system in gear with the main shaft and the governor respectively will then correspond to the centres of percussion and rotation of a simple body, and this relation will be mutual.
In such differential systems a constant force, , sufficient to keep the governor in a proper state of efficiency, is applied to the axis , and the motion of this axis is made to work a valve or a break on the main shaft of the machine. in this case is merely the friction about the axis of . If the moments of inertia of the different parts of the system are so arranged that , then the disturbance produced by a blow or a jerk on the machine will act instantaneously on the valve, but will not communicate any impulse to the governor.