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You substitute $\dot{\phi} = \frac{1}{T} \frac{d\phi}{d\tau}$. Now let's consider the dimensions \begin{align} [\dot{\phi}] &= [\frac{d\phi}{dt}] = \frac{rad}{s}\\ [\dot{\phi}] &= [\frac{1}{T} \frac{d\phi}{d\tau}] = \frac{1}{s} \cdot [\frac{d\phi}{d\tau}] \\ \Rightarrow [\frac{d\phi}{d\tau}] &= rad \end{align} and analog for $\ddot{\phi}$. ...


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Usually, a spatial nonlocality arises when there is a long-range interaction in a system. (Basically, an interaction, that decreases non-exponentally, is considered as a long-range interaction, for example, the interaction of electric or magnetic dipoles). The long-range interaction in a system results in a nonlocal response. This means that a field at point ...


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