Classical Mechanics (Kibble & Berkshire) · Problem 13.13

Hamilton's equations and phase space — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · hamiltons-principle

Problem

By using Hamilton's principle, show that, if the Lagrangian

L(\boldsymbol{q}, \dot{\boldsymbol{q}}, t)

is modified to

L'

by any transformation of the form

L' = L + \frac{d}{dt}\, g(\boldsymbol{q}, t),

then the equations of motion are unchanged.