vivitribal
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In general how do you demonstrate that a given Lagrangian equation provides the correct equation of motion?
Lagrangian and equation of motion
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Science Advisor
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By computing the equations of motion ? 
Daniel.
Daniel.
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The whole point of using the Lagrangian is that any physically possible motion must make the Lagrangian (Kinetic energy minus potential energy) an extremum. Apply "calculus of variations" (essentially the Euler-Lagrange equation) to the Lagrangian to derive the equations of motion.