Algebras of integrals

A classical theorem in mechanics states that a Hamiltonian which is invariant under a symmetry group admits additional integral s of motion. Thi s paper investigates the converse of the above theorem. If a Hamiltonian admits integrals then a symmetry can be constructed and the flaw studied on a quotient space. The quotient space is shown to be symplectic  and the resulting flow Hamiltonian. The constructions used are similar to the recent constructions of Nehoroshev, Marsden and Weinstein and Meyer.

The general theory presented is used to give an intrinsic derivation of Hamilton's equations of motion. Al so special local coordinates are given which display the integrals in a simple form.