Have you heard of the principle of least action?

The principle of least action suggests an alternative way to derive the equations of motion for a moving object. Instead of using Newton’s idea of F=m\alpha, one can instead try to find the path that minimizes the following integral

S=\int_{t_1}^{t_2}[KE-PE]dt

where KE = kinetic energy and PE = potential energy, 0\leq t_1\leq t_2

The reason for searching the path that minimizes that integral is simple; That’s the same path that the actual object will follow in real life. Isn’t this amazing? Nature is a “natural” optimization machine.

This idea is central in classical mechanics and the search for a path that minimizes a certain integral is something that I keep on seeing all over the place. So, here’s two suggested readings on this principle.

First, a lecture by Richard Feynman on the the least action principle and, for the people that want to look at more math, I recommend these notes by Daniel Baumann of DAMTP in Cambridge. Also, check his notes on the concepts in theoretical physics which seems like a fun class.

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