Lagrangian formalism is a technique using which we can obtain the time evolution of a dynamical system. Given a dynamical system, can we say whether or not we can write down a Lagrangian (solving it is another thing) i.e. can we say that a given dynamical system is in the realm of lagrangian dynamics (or is it invalid to ask such a question)?
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Related, and possible duplicate https://physics.stackexchange.com/q/1058/ – Jul 24 '17 at 14:06
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Possible duplicates: https://physics.stackexchange.com/q/3500/2451 , https://physics.stackexchange.com/q/4749/2451 , https://physics.stackexchange.com/q/283238/2451 and links therein. – Qmechanic Jul 24 '17 at 14:10