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Conservation and potential with non-cartesian forces
I understand how to determine if a force is conservative from
\begin{equation}
\nabla\times \mathbf{F}=0 \implies \mathbf{F}\text{ is conservative}
\end{equation}
When $F$ is in cartesian coordinates.
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Analogues to Hamilton's equations in Infinitesimal Canonical Transformations
This is from chapter 4 of David Tong's notes on Classical Dynamics (Hamiltonian Formalism).
Let's say you make an infinitesimal canonical transformation (with $\alpha$ as the infinitesimal parameter) ...
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