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## Homework Statement

Im trying to understand the Legendre transform from Lagrange to Hamiltonian but I don't get it. This pdf was good but when compared to wolfram alphas example they're slightly different even when accounting for variables. I think one of them is wrong. I trust wolfram over the pdf but I like the pdf approach better. How does the wolfram formula relate to Lagrange formula given by wolfram? for example

- f = L
- x = ?
- y = ?
- u = (p maybe ?)
- v = ?
- g = H

## Homework Equations

Equation 6 in the pdf says that its negative? It likes like they're saying g(arbitrary) is -H = (L-p qdot) therefore H = (p qdot - L) I am confused as to why it can be -H.

## The Attempt at a Solution

I attempted to do the matching above but I don't think I'm doing it right.