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The Kepler Problem S‐Sphere and the Kepler Manifold [PDF]
Meccanica, 1998 As an outcome of the author's previous work on unitary configuration space description of the classical Kepler problem [Celest. Mech. Dyn. Astron. 60, No. 3, 291-305 (1994; Zbl 0821.70005)], it is shown how the peculiar characterization of the Kepler orbits introduced by \textit{J. F. Carinena} et al. [Celestical Mech. Dyn. Astron. 52, No.
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Journal of Physics A: Mathematical and General, 1991 Summary: A class of dynamical systems is presented which includes, as special cases, both the (autonomous) Ermakov system and central force problems of Kepler type with angular dependence of the force. It is shown that all members of this class are linearizable up to a pair of quadratures.
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2018
Abstract This chapter considers Newton’s 1665 explanations of the dynamics in the laws governing the motion of a planet around the Sun, which were established by Johannes Kepler in 1618. The first law states that the motion is planar and the trajectories are ellipses.
Jean-Philippe Uzan, Nathalie Deruelle
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Abstract This chapter considers Newton’s 1665 explanations of the dynamics in the laws governing the motion of a planet around the Sun, which were established by Johannes Kepler in 1618. The first law states that the motion is planar and the trajectories are ellipses.
Jean-Philippe Uzan, Nathalie Deruelle
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Stabilization of Kepler's problem
Celestial Mechanics, 1977A regularization of Kepler's problem due to Moser (1970) is used to stabilize the equations of motion. In other words, a particular solution of Kepler's problem is imbedded in a Liapunov stable system. Perturbations can be introduced into the stabilized equations.
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Journal of Dynamical and Control Systems, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the inverse Kepler problem [PDF]
European Journal of Physics, 1985 Much useful information-and not only the inverse square law force-can be extracted from Kepler's law. A very simple treatment is proposed.
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2010
The two-body problem is the study of the motion of two material points \( \mathcal{P}_1 \) and \( \mathcal{P}_2 \), with masses respectively m1 and m2; when the two bodies are subject to the mutual gravitational attraction one speaks of Kepler’s problem, whose dynamics is described by the three so-called Kepler’s laws (see, e.g., [157]).
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The two-body problem is the study of the motion of two material points \( \mathcal{P}_1 \) and \( \mathcal{P}_2 \), with masses respectively m1 and m2; when the two bodies are subject to the mutual gravitational attraction one speaks of Kepler’s problem, whose dynamics is described by the three so-called Kepler’s laws (see, e.g., [157]).
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Minimizers for the Kepler Problem
Qualitative Theory of Dynamical Systems, 2020We characterize the minimizing geodesics for the Kepler problem endowed with the Jacobi-Maupertuis metric. We focus on the positive energy case, but do all energies. The more complicated negative energy case was solved in Jacobi (Crelles J 17:68–82, 1837.
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Physical Review D, 1971
Relativistic quantum field theory is used as a starting point to construct a classical, completely relativistic theory of planetary orbits.
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Relativistic quantum field theory is used as a starting point to construct a classical, completely relativistic theory of planetary orbits.
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Journal of Mathematical Physics, 2000
Using the idea that the symmetry generators commuting with a Landau-like Hamiltonian containing non-Abelian gauge fields will be matrix-valued differential operators, we reconsider the eigenvalue problem of the five-dimensional (5-D) Kepler problem on a SU(2) instanton background. We quickly reproduce the result of Pletyukhov and Tolkachev [J.
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Using the idea that the symmetry generators commuting with a Landau-like Hamiltonian containing non-Abelian gauge fields will be matrix-valued differential operators, we reconsider the eigenvalue problem of the five-dimensional (5-D) Kepler problem on a SU(2) instanton background. We quickly reproduce the result of Pletyukhov and Tolkachev [J.
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