PHYS2113 2023 Video 3 -- Calculus of Variations (Part 1)

This lecture is the first in a series on Lagrangian mechanics looking at the calculus of variations. This first half we work on obtaining the Euler-Lagrange equations by the standard calculus of variations approach.

Note: Apologies for minor typo at 20:24, should be df/dalpha not df/dx.

Lecturer: Prof. Adam Micolich

Background: 立ち飲み Beer Boy, Naka Meguro, Tokyo, Japan.

[peterwan]

At 32 minutes 45 seconds, to force dS/d(alpha) to zero, you set part of the integrand to zero. This, of course can do it, but is that too drastic a measure? The fact that the integral goes to zero does not necessarily require the integrand goes to zero. It is just the sum that needs to be zero at the end. For example, if I integrate sin(x) over one cycle, I get zero because the positive half cancel the negative half. However, sin(x) is not zero in the domain from 0 to 2 pi.