Question

What is the advantage of lagrangian equation?

Answer 1

1) First state my qualifications which are enough calculus and physics to get the intent and also state that this is clearly outside my current field and so I claim no qualification as a current practitioner although I may dig around in this for obvious to me reasons. 
2) Second, perform my engineering duty which is research of any question posed to create at least an estimate of an answer if possible which we all should be able to do. Thus, a very short search finds that Wikipedia is the reference! Their answer as follows: It provides a simplification of the effort required to reach a solution, at least to some problems.