What is it about?

The importance of the Kepler problem is not only related to its varied applications in different fields of science, but rather to its use in developing some mathematical methods. Thus, this problem has been used to develop new methods in classical mechanics, like Hamiltonian mechanics, the Hamilton-Jacobi equation, Lagrangian mechanics and action-angle coordinates. Furthermore, the Kepler and simple harmonic oscillator problems are two of the most fundamental problems in classical mechanics. They are also the only integrable dynamical systems which have closed orbits for open sets of possible initial conditions.

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Why is it important?

We describe the global dynamics of the Hamiltonian system of relativistic Kepler problem

Perspectives

The solution of the Kepler problem allowed researchers to investigate the unperturbed and the perturbed Lagrange’s planetary motion. Thus, these motions were clarified entirely by the classical mechanics and the Newton’s law of universal gravitation

Elbaz I. Abouelmagd
National Research Institute of Astronomy and Geophysics (NRIAG)

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This page is a summary of: The dynamics of the relativistic Kepler problem, Results in Physics, December 2020, Elsevier, DOI: 10.1016/j.rinp.2020.103406.
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