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Research Article | Open Access

Normalization and reduction of the Stark Hamiltonian

University of Calgary, Calgary, Alberta, T2N 1N4, Canada
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Abstract

We detail a calculation of the second order normal form of the Stark effect Hamiltonian after regularization, using the Kustaanheimo-Stiefel mapping. After reduction, we obtain an integrable two degree of freedom system on S h 2 × S h 2 , which we reduce again to obtain a one degree of freedom Hamiltonian system.

Keywords

Kustaanheimo-Stiefel normalizationStark Hamiltonianreduction of symmetries
CLC number: 70K45

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Communications in Analysis and Mechanics
Volume 15 Issue 3,
September 2023
Pages 457-469
DOI: 10.3934/cam.2023022

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Cushman R. Normalization and reduction of the Stark Hamiltonian. Communications in Analysis and Mechanics, 2023, 15(3): 457-469. https://doi.org/10.3934/cam.2023022

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Received: 03 February 2023
Revised: 01 August 2023
Accepted: 03 August 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)