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Variational principles such as hamilton's principle are used to state the laws of physics. To my knowledge, all of classical theory (including GR) can be stated this way. The resulting DE can then be found using the euler-lagrange equations.

My question is twofold.

1. Can all possible laws of physics be stated this way in principle? Not just all known laws, or all 'true' laws. Can all wild and crazy differential equations for the position of a particle as a function of time be derived from some judicious choice of the Lagrangian.

2. If no. What specific limitations are imposed on the laws of physics if we demand that they are derivable from variational principles?

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# Variational principles in physics

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