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Answer by Igor Khavkine for Classification of Lagrangians with given...
In a sense, all the Lagrangians giving the same Euler-Lagrange equations are exhausted by transformations of your type (b), which adds a total derivative/total divergence/boundary term/......
View ArticleAnswer by Ben McKay for Classification of Lagrangians with given...
This problem is discussed in Bryant, Griffiths, Hsu, Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, for Lagrangians for scalar fields.
View ArticleClassification of Lagrangians with given Euler-Lagrange equations
In (mathematical) physics the equations of motion of a system of particles are often interpreted as Euler-Lagrange equations for appropriate Lagrangian $L=L(x,\dot x,t)$ where $x$ is a collection of...
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