A geometric derivation of Noether's theorem

Nother's theorem is a cornerstone of analytical mechanics, making the link between symmetries and conserved quantities. In this article, I propose a simple, geometric derivation of this theorem that circumvents the usual difficulties that a student of this field usually encounters. The derivation is based on the integration of the differential form dS = pdq - Hdt, where S is the action function, p is the momentum, and H the Hamiltonian, over a closed path.