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Mathematics of classical mechanics, including Hamiltonian mechanics, Lagrangian mechanics, applications of symplectic geometry to mechanics, deterministic chaos, resonance etc.

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How to interpret the vector fields $F_p(x,u,Du)$ in a Lagrangian optimization problem

There is the following interpretation coming from physics and continuum mechanics, which is a bit too long for a comment but might be helpful: If you think of $\mathcal{F}$ as an energy that you want …
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