The Quantity of Motion
On the other hand, in the case of a harmonic oscillator,
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On the other hand, in the case of a harmonic oscillator, consisting of two masses connected by a spring, the total kinetic energy does vary cyclically, and yet we maintain conservation of energy by including the potential energy contained in the spring. Would it be possible to define such a thing as �potential momentum�, analogous to potential energy, for the case of the revolving globes? The rod holding the globes together is in tension, resisting the inertial tendency of the globes to fly apart, but this tension is constant, so it seems we cannot attribute any varying �potential momentum� to the rod. However, the tension in the rod is alternately parallel and perpendicular to the aggregate direction of motion, so if we were determined to conserve absolute momentum, we might define the potential momentum of tension as a function of the orientation of that tension relative to the direction of motion. We could assert that the potential momentum of a given amount of stress in motion is greater when the stress is perpendicular to the direction of motion than when it is parallel to the direction of motion. The spatial extent of the rod behaves in just this way when special relativity is taken into account, so at least some of the variation in �potential momentum� could be associated with the variation in length. But this doesn�t seem to lead to any natural concept of potential momentum that would keep the total absolute momentum constant.
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