Question: Consider a differentiable function (V(q)) of a generalized coordinate (q). Consider the Lagrangian (L=(1 / 12) m^{2} dot{q}^{4}+m dot{q}^{2} V(q)-V^{2}(q)). Show that this system is
Consider a differentiable function \(V(q)\) of a generalized coordinate \(q\). Consider the Lagrangian \(L=(1 / 12) m^{2} \dot{q}^{4}+m \dot{q}^{2} V(q)-V^{2}(q)\). Show that this system is equivalent to a much simpler Lagrangian for a particle moving in a potential.
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