Must there exist a Lagrangian for any 2nd order ordinary derivative equation?

Asked Apr 19 '16 at 04:18

Active Apr 19 '16 at 05:12

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We know if there exist a Lagrangian of some ODE, then it must exist many equivalent Lagrangian.

My question:

Then must there exist a Lagrangian for any 2nd order ODE? If not, do we have some necessary or sufficient conditions for a dynamical system which can be described by some Lagrangian?

edited Apr 19 '16 at 05:12

Qmechanic

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asked Apr 19 '16 at 04:18

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This is very related: http://math.stackexchange.com/q/1333379/ – Sidharth Ghoshal Apr 19 '16 at 04:19
Possible duplicates: http://physics.stackexchange.com/q/20188/2451 , http://physics.stackexchange.com/q/3500/2451 , http://physics.stackexchange.com/q/20298/2451 and links therein. – Qmechanic Apr 19 '16 at 05:15

Must there exist a Lagrangian for any 2nd order ordinary derivative equation?

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