If you read some introductory mechanics text like David Morin's Introduction to Classical Mechanics about Euler Lagrange Equations you get a large amount of simple examples like the "moving plane" (Problem 6.1 in the link above) or the double pendulum of how to apply the Euler Lagrange equations.

However something like the moving plane example or the double pendulum looks for me like a nice toy example.

Are any of those typical simple examples relevant in modelling something in engineering, sports science or something like that? If not are there any simple examples for the applications of the Euler Lagrange equations which are relevant in this sense?

By "simple" I mean something like the double pendulum or even more simple (in deriving the equations of motion; not solving it); the more simple the example the better.

P.S. I am not sure it the question is more appropriate on engineering.sx. But I cannot crosspost. If you think it should be migrated, please let my know.

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    $\begingroup$ This post (v2) seems like a list question. $\endgroup$ – Qmechanic Apr 19 '16 at 20:00
  • $\begingroup$ I'm sorry, but it's not clear to me what you're asking. Are you saying that the moving plane and double pendulum are too simple or not simple enough? Those both exist in real-world engineering context. But you can also derive the really simple equations like a ball on a parabola. You'll usually see Euler-Lagrange equations applied to more complicated systems than that, just because they're better at dealing with subtleties that don't arise in simple systems. $\endgroup$ – Mike Apr 19 '16 at 20:08
  • $\begingroup$ Most simulatons use the transformed equations, in Hamiltonian form, because they are linear. As such you find tmem used extensively in engineering applications. For continuum systems the finite element methods are derived from Hamiltonian methods. $\endgroup$ – Peter Diehr Apr 19 '16 at 20:21
  • $\begingroup$ @Mike: The complexity should be like the double pendulum or the moving plane or more simple. $\endgroup$ – Julia Apr 20 '16 at 5:35

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