We always go in one direction, from Lagrangian to equations of motion (classical mechanics). But is it possible to go the opposite way, from equation of motion to Lagrangian? Suppose we have an equation of motion $$ f(q,\dot{q},\ddot {q})=0. $$ Is there a way to tell if there exist a Lagrangian that generates the equation of motion? And if there is one, how can we find it? (I am aware it is not going to be a unique solution)
Asked
Active
Viewed 20 times
