Normalization and reduction of the Stark Hamiltonian (Q6579788)

In Section 2, the set up of the paper is presented. The Stark Hamiltonian is recalled. Using the Kustaanheimo-Stiefel mapping, it is transformed into the regularized Stark Hamiltonian.\N\NIn Section 3, the first-order normal form of the regularized Stark Hamiltonian is derived. Then, in Section 4, the second-order normal form \(\mathcal{H}_{nf}^{(2)}\) is obtained.\N\NIn Section 5, the normal form of the above-mentioned Hamiltonian \(\mathcal{H}_{nf}^{(2)}\) is computed, and in the next section, it is reduced on \(S_h^2\times S_h^2,\) resulting in the Hamiltonian \(\widehat{\mathcal{H}}.\)\N\NIn Section 7, the completely integrable Hamiltonian system \((\widehat{\mathcal{H}},S_h^2\times S_h^2,\{.,.\})\) is presented. Moreover, this system is reduced to a one-degree-of-freedom Hamiltonian system.\N\NAs the author points out, ``our procedure of regularization, pulled back by the KS map, normalization and reduction, may be used to study three-degree-of-freedom perturbed Keplerian systems.''