Patrick414159
New member
- Joined
- Jan 1, 2021
- Messages
- 3
I have a Euler-Lagrange related problem. Specifically, my text book skips a few steps that I cannot bridge without some help. The problem is this:
Given a function f(y(x), y'(x)), the Euler-Lagrange equation reduces (in differential form) to:
No problem, I can show this. My book then says:
"Since f does not explicitly depend on "x",
I apologize for the weird d/dx on the left, it is a total derivative wrt x. Mathematica insists on formatting it that way for some reason. Anyway, I cannot show that the lhs = the rhs in the second equation, despite many pages of trying which I will omit here. Can anyone show how the second equation is justified step-by-step?
Thanks in advance.
Patrick
Given a function f(y(x), y'(x)), the Euler-Lagrange equation reduces (in differential form) to:
No problem, I can show this. My book then says:
"Since f does not explicitly depend on "x",
I apologize for the weird d/dx on the left, it is a total derivative wrt x. Mathematica insists on formatting it that way for some reason. Anyway, I cannot show that the lhs = the rhs in the second equation, despite many pages of trying which I will omit here. Can anyone show how the second equation is justified step-by-step?
Thanks in advance.
Patrick