What is the shortest path between two points in space? Solution using the calculus of variations.

Here is an introduction to the Euler-Lagrange equation to find the shortest path between two points in flat 2d space.

[thevegg]

I’m wondering why the first half of the right hand term of the Euler LeGrange equation isn’t d/dx F instead of d/dx.
I appreciate the visit though thank you !

[thevegg]

How do you integrate along the path when you don't know what the equation of that curvy path is?

[thevegg]

Is there another way to do this other than what you’ve shown because I see a lot of presenters using a a second path that varies slightly from the original path and using that somehow to find the straight line on a flat surface between two points.
I don’t see any variation in the path in your presentation

[oooo]

The partial of f wrt y prime was 0, but you said the partial of f wrt y was zero also?