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For questions involving the Lagrangian formulation of a dynamical system. Namely, the application of an action principle to a suitably chosen Lagrangian or Lagrangian Density in order to obtain the equations of motion of the system.
11
votes
Accepted
Why does the partial derivative with respect to $x$ of a function depending only on $\dot{x}...
This is a common point of confusion when one gets started in Lagrangian mechanics. The important thing to notice is that we are taking partial derivatives, not full derivatives with respect to $x$.
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2
votes
Is the Lagrangian in the Standard Model exact or approximate?
The standard model Lagrangian does not model quantum gravity nor dark matter (as far as we know), hence it is certainly not an 'exact' description of the universe anyway.
However, your question is w …