I am only 15 year old,but I am terribly interested in physics. Once I was watching some kind of interesting lecture,and I came across Lagrangian-mechanics. What is it? How is it different from Newtonian mechanics? Does it "tell us" any "new" things? I would really appriciate if someone could show this to me.

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    $\begingroup$ Possible duplicate of What is the difference between Newtonian and Lagrangian mechanics in a nutshell? $\endgroup$ – João Vítor G. Lima Mar 5 '19 at 17:46
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    $\begingroup$ Relevant links: Hamiltonian mechanics and Lagrangian mechanics $\endgroup$ – jacob1729 Mar 5 '19 at 17:46
  • $\begingroup$ If you go back to what Lagrange actually did (rather than what other people did later on) the basic difference is the approach to solving problems. Newton considered all the interactions between the bodies in a system, using force, mass, and acceleration. Lagrange instead considered the energy of the bodies and the work done on the system. Those ideas can tell you a lot of useful things about how the system behaves without having to bother about all the individual forces and accelerations that are happening inside it. $\endgroup$ – alephzero Mar 5 '19 at 18:11