Notes on Cambridge Maths

Something looks off?

The button will add this page to my log of things to fix. Use it for broken links, equations not rendering correctly, etc.
Submit other issues on GitHub.

Euler-Lagrange

To minimize:


over , need to solve Euler-Lagrange:


If is a vector (or there are multiple functions of involved), then get multiple equations:

First integrals

If :


If :

Multivariable case

Suppose we now have where . The equation becomes:

Higher derivative case

Suppose now :


Note that we can rewrite:

Something looks off?

The button will add this page to my log of things to fix. Use it for broken links, equations not rendering correctly, etc.
Submit other issues on GitHub.

Graph View

Backlinks