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.