Classical Mechanics (Kibble & Berkshire) · Problem 14.1
The general theory of small oscillations — T.W.B. Kibble, F.H. Berkshire
Physics — Mechanics · legendre-transform
Problem
Find the Legendre transform G(v1,v2,w) of the function
F(u1,u2,w)=2u12−3u1u2+u22+3wu1,
where w is a passive variable. Verify that ∂F/∂w=−∂G/∂w.