Normalization and reduction of the Stark Hamiltonian

Richard Cushman; Richard Cushman

doi:10.3934/cam.2023022

Communications in Analysis and Mechanics

2023, Volume 15, Issue 3: 457-469. doi: 10.3934/cam.2023022

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Normalization and reduction of the Stark Hamiltonian

Richard Cushman ^,

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

Received: 03 February 2023 Revised: 01 August 2023 Accepted: 03 August 2023 Published: 07 August 2023
70K45

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^2_h \times S^2_h $, which we reduce again to obtain a one degree of freedom Hamiltonian system.
- Kustaanheimo-Stiefel normalization,
- Stark Hamiltonian,
- reduction of symmetries
Citation: Richard Cushman. Normalization and reduction of the Stark Hamiltonian[J]. Communications in Analysis and Mechanics, 2023, 15(3): 457-469. doi: 10.3934/cam.2023022

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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^2_h \times S^2_h $, which we reduce again to obtain a one degree of freedom Hamiltonian system.

References

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[2]	R. Cushman, The geometry of the Kustaanheimo-Stiefel mapping, preprint, $\texttt{arXiv: 2205.08485}$.
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[4]	J. Lagrange, Méchanique Analytique, Courcier, Paris, 1788.
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