scholarly journals Regularized variational principles for the perturbed Kepler problem

2021 ◽  
Vol 383 ◽  
pp. 107694
Author(s):  
Vivina Barutello ◽  
Rafael Ortega ◽  
Gianmaria Verzini
Keyword(s):  
Variational Principles ◽  
Kepler Problem ◽  
Perturbed Kepler Problem

An expectation value formulation of the perturbed Kepler problem

1987 ◽  
Vol 55 (7) ◽  
pp. 627-631 ◽  
Author(s):  
Lorenzo J. Curtis ◽  
Roger R. Haar ◽  
Martin Kummer
Keyword(s):  
Kepler Problem ◽  
Expectation Value ◽  
Perturbed Kepler Problem

scholarly journals From geodesics of the multipole solutions to the perturbed Kepler problem

2010 ◽  
Vol 82 (10) ◽  
Author(s):  
J. L. Hernández-Pastora ◽  
J. Ospino
Keyword(s):  
Kepler Problem ◽  
Perturbed Kepler Problem

scholarly journals Quaternions and the perturbed Kepler problem

2006 ◽  
Vol 95 (1-4) ◽  
pp. 201-212 ◽  
Author(s):  
Jörg Waldvogel
Keyword(s):  
Kepler Problem ◽  
Perturbed Kepler Problem

C1 non-integrability of a hydrogen atom in a circularly polarized microwave field

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Juan Guirao ◽  
Miguel López ◽  
Juan Vera
Keyword(s):  
Hydrogen Atom ◽  
Microwave Field ◽  
Kepler Problem ◽  
Main Tool ◽  
Averaging Theory ◽  
Circularly Polarized ◽  
Numerical Evidence ◽  
Perturbed Kepler Problem ◽  
Analytical Proof

AbstractBarrabés et al. [Physica D, 241(4), 333–349, 2012] consider the problem of the hydrogen atom interacting with a circularly polarized microwave field modeled as a planar perturbed Kepler problem. For different values of the parameter, the authors offer some numerical evidence of the non-integrability of this problem. The objective of the present work is to give an analytical proof of the C1 non-integrability of this problem for any value of the parameter using the averaging theory as a main tool.

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