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 circumvent the usual difficulties that a student of this field usually encounters. The derivation is based on the integration the differential form dS=pdq-Hdt, where S is the action function, p the momentum and H the Hamiltonian, over a closed path.