Sign up ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Is there a systematic procedure to generally obtain an appropriate action that corresponds to any given equations of motion (if I know that it exists)?

share|cite|improve this question
Related: – Qmechanic Nov 1 '12 at 20:27

1 Answer 1

up vote 3 down vote accepted

In general, this is difficult, as the same dynamics can be written in many different forms.

In concrete cases, I'd do one of the following:

  1. Work out the Hamiltonian (i.e., look for conserved quantities of a reasonably simple form), then work out pairs of conjugate variables that allow you to write the equation of motion in Hamiltonian form, then invert the canonical formalism to get the Lagrangian.

  2. Write down the most general combinations of terms whose functional derivatives resemble those in the given equation, and then try to match terms, accounting for a possible (but assumed simple) integrating factor.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.