Constrained normalization of Hamiltonian systems and perturbed Keplerian motion (Q1084886)

This paper develops a theory for normalising constrained Hamiltonian systems. Consider a Hamiltonian H on \({\mathbb{R}}^{2n}\) with standard symplectic form \(\omega\). For a symplectic submanifold M, the constrained Hamiltonian system is \(H| M\) on M with form \(\omega| M\). A normalisation algorithm is given for H which on M restricts to a normalisation of the constrained system. More than half the paper is given to applying these ideas to perturbed Kepler systems, with details worked out for the Lunar problem, and part of artificial satellite theory.