I am in high school and I need to solve lots of problems which involve spring-block systems, pendulums, damped oscillations and so on. I am learning Lagrangian mechanics and I am already quite proficient in solving these problems with Newtonian mechanics by resolving the forces and by energy conservation. I think that the force method is time consuming. I have heard several people say that Lagrangian mechanics can very easily give the equations of motion and I was hoping someone with first-hand experience could tell if I should solve these types of problems with Lagrangian mechanics.

  • 4
    $\begingroup$ This is primarily opinion-based, since, for instance, I like Hamiltonian mechanics far better. The "best" way to do a problem is not objective. $\endgroup$ – ACuriousMind Dec 13 '15 at 16:28
  • 2
    $\begingroup$ The real power of Lagrangian mechanics comes when you have to solve problems with constrained motion, e.g. a ball circling in a hemispherical bowl. In this case, finding the form of the force and using Newtonian mechanics is a mess. $\endgroup$ – nightmarish Dec 13 '15 at 16:28
  • $\begingroup$ @failexam I am comfortable with writing force equations, but sometimes solving them is tedious. So, I was wondering whether it would be easier to solve problems of the type I have mentioned using Lagrangian mechanics, assuming I am quite good at math. $\endgroup$ – ShankRam Dec 13 '15 at 16:32
  • 2
    $\begingroup$ @ShankRam "I am comfortable with writing force equations, but sometimes solving them is tedious": the equations are independent of the formalism; they only depend on the coordinates you choose. If your question is about which methods leads to the simpler equations, then the answer is: they both lead to the same set of equations. $\endgroup$ – AccidentalFourierTransform Dec 13 '15 at 16:40
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/8903/2451 and links therein. $\endgroup$ – Qmechanic Dec 13 '15 at 19:51