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Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].

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Deducing equation of motion for a free particle using the form of the Lagrangian

The point is, the function you mentioned is non differentiable at a single point which we can disregard by just restricting our domain of interest to be the complement of that point. The lagrangian in …
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How to show that the Hamiltonian $H$ is invariant under flow generated by $F$?

It follows directly from the poisson bracket relation $\{{F,H}\}=-\{{H,F}\}=0$ This says that $F$ is invariant under the flow of $H$ and $H$ is invariant under the flow of $F$. If you want an explicit …
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Help with geometric view of conjugate momenta and Legendre transformation

Equation (3) is the correct one. The first thing one needs to remember in Lagrangian mechanics is that $L$ is a function of position and velocities treated as independent variables. So when we say $L$ …
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