Canonical Transformation - Motion As A Canonical Transformation

Motion As A Canonical Transformation

Motion itself (or, equivalently, a shift in the time origin) is a canonical transformation. If and, then Hamilton's principle is automatically satisfied

$\delta \int_{t_{1}}^{t_{2}} \left dt = \delta \int_{t_{1}+\tau}^{t_{2}+\tau} \left dt = 0$

since a valid trajectory should always satisfy Hamilton's principle, regardless of the endpoints.

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