1. The problem statement, all variables and given/known data 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 also in the original pdf it states H is negative when H = L - p qdot. Why? Mathematically and physically why is this, and why does the Hamiltonian equations H = p qdot- L (in one dimension) equal to just the derivative of H in respect to q and p? 2. Relevant 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) Im confused as to why it can be -H. 3. The attempt at a solution I attempted to do the matching above but I don't think I'm doing it right.