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I am very puzzled by the following remark on p.346 in Arnold's book "Mathematical methods of classical mechanics": Another method of construction the same symplectic structure on complex ...

I am trying to calculate classical trajectories for a single a ion and a single electron inside an RF trap. Therefore, I am dealing with a two-body system that possesses: Coulomb potential with a ...

The Euler–Lagrange equation is an equation satisfied by a function $q$, which is a stationary point of the functional $S(\boldsymbol q) = \int_a^b L(t,q(t),\dot{q}(t))\, \mathrm{d}t$ Say we have an ...

I originally posted this question on Physics SE, but I think it is more like a math question since I need rigorous justification. Could anyone please provide any insight to the below question: Let us ...

Let $Q$ be a manifold, and let $X_{EL}$ be a second order vector-field on $TQ$ derived from the Euler-Lagrange equation, $$ \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q} } \right) - \frac{ \...

I already asked this in the physics forum but without much attention, so I thought it might attract more attention here. Is there an integral expression for the Poisson bracket that can be derived ...