The Trick

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'The Trick' refers to the blatantly cheeky act of multiplying a variable by its derivative to integrate it. Examples are abound in classical mechanics, such as in the example below.

Suppose I need to find K, the Kinetic energy, and I have \ddot{r}.

Then,

\dot{r} \ddot{r} = \frac{1}{2} \frac{\partial}{\partial t}{\dot{r}^2} = \frac{1}{2}v^2 = \frac{E}{m}.

If we're doing quantum or special relativity, r can be replaced with p the momentum. Examples of the trick are numerous and wonderful.

To be completed.

Much of the early history of the trick was lost, but like most everything else it was probably used by Newton. It's canonical name was, as far as can be recalled, given by Austin Roach (Plasmagician, entering class of 2005) during a prelim studying session, where Jeremy Olson voiced skepticism.

This page was recovered in October 2009 from the Plasmagicians page on The_Trick dated 03:10, 30 September 2006.

Retrieved from "https://qed.princeton.edu/main/PlasmaWiki/The_Trick"
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