What are the advantages in applying lagrange's equations instead of Newtons law?
I was intrigued by the lack of an overwhelming number of responses in the last 2 hours since this was posted. I only have to do two things to provide a response:
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.
Lagrangian mechanics
From Wikipedia, the free encyclopedia
The use of generalized coordinates may considerably simplify a system’s analysis. For example, consider a small frictionless bead traveling in a groove. If one is tracking the bead as a particle, calculation of the motion of the bead using Newtonian mechanics would require solving for the time-varying constraint force required to keep the bead in the groove. For the same problem using Lagrangian mechanics, one looks at the path of the groove and chooses a set of independent generalized coordinates that completely characterize the possible motion of the bead. This choice eliminates the need for the constraint force to enter into the resultant system of equations. There are fewer equations since one is not directly calculating the influence of the groove on the bead at a given moment.