Normalization and reduction of the Stark Hamiltonian
type: Item
instance of: scholarly article
title: Normalization and reduction of the Stark Hamiltonian
author: Richard Cushman
published in: Communications in Analysis and Mechanics
publication date: 2024-07-26T00:00:00Z
review text: 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.''
reviewed by: Cristian Lăzureanu
Mathematics Subject Classification ID: 70H33
Mathematics Subject Classification ID: 70H06
Mathematics Subject Classification ID: 70K45
zbMATH DE Number: 7887820
zbMATH Keywords: second-order normal form
zbMATH Keywords: Kustaanheimo-Stiefel normalization
zbMATH Keywords: symmetry reduction
zbMATH Keywords: complete integrability
MaRDI profile type: Publication
cites work: Monodromy in the hydrogen atom in crossed fields
cites work: Complete closed-form solutions of the Stark problem
cites work: Reduction and regularization of the Kepler problem
DOI: 10.3934/CAM.2023022
description: scientific article; zbMATH DE number 7887820