Theory of Electricity And Magnetism

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289 for the given system. From the slow variation of the k's it follows that they can be regarded as constant during a considerable lapse of time and thus the motion itself as approximately cyclic (during that period). After a greater lapse of time the parameters k will assume other values, and the motion can again be regarded as cyclic. We can, therefore, define a cycle as a system containing only cyclic and slowly changing coordinates or parameters. By equation (2) our general equations of mo...tion (1) for cycles reduce to where L and K denote the forces that tend to increase the cyclic coordinates I and the parameters k respectively. The simplest case of cyclic motion is where we have a single cyclic coordinate I ; such a system is called a monocycle. The positions of all parts of such a system, except those due to the slow variation of the parameters k, will then be determined by the position of a single driving-point defined by that coordinate. If the driving- point is at rest, all parts of the system will remain at rest, whereas, if it is moving with a given velocity I', the motions of all its masses will be determined by that velocity.

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