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8.3: Varying Both Ends

( \newcommand{\kernel}{\mathrm{null}\,}\)

The argument given above for the incremental change in action from varying the endpoint is clearly equally valid for varying the beginning point of the integral (there will be a sign change, of course), so

dS(q(2)i,t2,q(1)i,t1)=ip(2)idq(2)iH(2)dt2ip(1)idq(1)i+H(1)dt1

The initial and final coordinates and times specify the action and the time development of the system uniquely.

(Note: We’ll find this equation again in the section on canonical transformations -- the action will be seen there to be the generating function of the time-development canonical transformation, this will become clear when we get to it.)


This page titled 8.3: Varying Both Ends is shared under a not declared license and was authored, remixed, and/or curated by Michael Fowler.

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