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Noether’s Theorems and Symmetry

Prof. Dr. John H. Maddocks

Perhaps the biggest impact of Noether in applied mathematics is her work relating continuous symmetries in dynamical systems to the existence of conservation laws. These results continue to this day to lead to original research. I will give one such example from my own work, in which Noether’s Theorem allows constrained Lagrangian dynamics to be written as an unconstrained Hamiltonian system in which the constraints are transformed to integrals of the motion. I will illustrate the general approach in the simple example of the spherical pendulum, so that only elementary calculus is required to understand the result.