Equality modulo equations of motion [closed]

Question

What does Qmechanic mean by “equality modulo equations of motion” when talking about Lagrangian formulation/formalism and so on?

Answer 1

I guess I should answer this :)

In the context of the Lagrangian formalism the equations of motion (EOM) refer to Euler-Lagrange (EL) equations.

The phrase "equality modulo EOM" means that a left-hand side is equal to a right-hand side of an equation if one uses the EOM.

It is often important to keep track of when one uses EOM. Sometimes one is not allowed to assume the EOM. A common error is a premature use of EOM in the stationary action principle. For an example of what can go wrong, see this or this Phys.SE posts.

See also this related Phys.SE post.