The Planetary Model as a Dynamical Kepler Problem

2019 ◽  
pp. 60-75
Author(s):  
Nicolae Mazilu ◽  
Maricel Agop ◽  
Ioan Mercheş
Keyword(s):  
Kepler Problem ◽  
Planetary Model

Constant fields

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Fine Structure ◽  
Inertial Frame ◽  
Kepler Problem ◽  
Coulomb Field ◽  
Spin Coupling ◽  
Planetary Model ◽  
Rutherford Scattering ◽  
Lorentz Equation ◽  
Basic Ideas ◽  
A Charge

This chapter reviews the basic ideas of electrostatics (Coulomb’s law) and magnetostatics (the Biot–Savart law). It studies the motion of a charge in a Coulomb field in detail. The chapter shows how the motion of a charge q in the Coulomb field of a charge Q held fixed at the origin of an inertial frame is governed by the Lorentz equation. Moreover, it can be solved like the Kepler problem discussed in the previous Book. Next, the chapter discusses the Rutherford scattering formula which established the ‘planetary’ model of the atom, the Bohr–Sommerfeld quantization which displayed the limits of the theory, and finally the spin coupling explaining the atomic fine structure.

The Higgs algebra and the Kepler problem inR3

2000 ◽  
Vol 33 (22) ◽  
pp. 4073-4079 ◽  
Author(s):  
V V Gritsev ◽  
Yu A Kurochkin
Keyword(s):  
Kepler Problem ◽  
Higgs Algebra

Remarks on the geometric quantization of the Kepler problem

1988 ◽  
Vol 16 (3) ◽  
pp. 189-197 ◽  
Author(s):  
Giuseppe Gaeta ◽  
Mauro Spera
Keyword(s):  
Kepler Problem ◽  
Geometric Quantization

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

GLOBAL BEHAVIOR OF THE CHARGED ISOSCELES THREE-BODY PROBLEM

1994 ◽  
Vol 04 (04) ◽  
pp. 865-884 ◽  
Author(s):  
PAU ATELA ◽  
ROBERT I. McLACHLAN
Keyword(s):  
Bifurcation Diagram ◽  
Periodic Orbits ◽  
Body Problem ◽  
Kepler Problem ◽  
Global Bifurcation ◽  
Three Body Problem ◽  
Anisotropic Kepler Problem ◽  
The One ◽  
Three Body ◽  
Limiting Value

We study the global bifurcation diagram of the two-parameter family of ODE’s that govern the charged isosceles three-body problem. (The classic isosceles three-body problem and the anisotropic Kepler problem (two bodies) are included in the same family.) There are two major sources of periodic orbits. On the one hand the “Kepler” orbit, a stable orbit exhibiting the generic bifurcations as the multiplier crosses rational values. This orbit turns out to be the continuation of the classical circular Kepler orbit. On the other extreme we have the collision-ejection orbit which exhibits an “infinite-furcation.” Up to a limiting value of the parameter we have finitely many periodic orbits (for each fixed numerator in the rotation number), passed this value there is a sudden birth of an infinite number of them. We find that these two bifurcations are remarkably connected forming the main “skeleton” of the global bifurcation diagram. We conjecture that this type of global connection must be present in related problems such as the classic isosceles three-body problem and the anisotropic Kepler problem.

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