Let ?s : C _R ? C _R be a dynamical symmetry of a system with Lagrangian L, with generators ua….

Let ?s : C _R ? C _R be a dynamical symmetry of a system with Lagrangian L, with generators ua. Show that under the action of ?s for small s, the change in ?L/?va along a kinematic trajectory is to the first order in s, where Deduce that And Show that Hence show that if qa = qa(t) is a solution of Lagranges equations, then so is qa = qa(t)+sua ‘ q(t), t( , to the first order in s. Deduce that if ?s is a dynamical symmetry, then it maps dynamical trajectories in C _R to dynamical trajectories.

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