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\[ \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q}} \right) - \frac{\partial L}{\partial q} = 0 \] where: \(L(q, \dot{q}, t)\) is the Lagrangian, typically defined as the difference between kinetic and potential energy, \(q(t)\) represents the generalized coordinate, \(\dot{q}\) is
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