Calculus of Variations Part 2: Lines, Bubbles, and Lagrange

In the first part, we discussed the idea of a functional, what it means, and how to find its extrema using the calculus of variations. However, those equations don’t really capture how amazing and applicable calculus of variations really is so the following will be some examples of this. In fact, the drawn out results from the posts The Shape of a String and The Lagrangian are just two cases of the one equation.

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