Variable Step Hybrid Block Method for the Approximation of Kepler Problem
Fractal and Fractional, 2022 In this article, a variable step size strategy is adopted in formulating a new variable step hybrid block method (VSHBM) for the solution of the Kepler problem, which is known to be a rigid and stiff differential equation.
Joshua Sunday +2 more
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The symmetry of the Kepler problem, the inverse Ligon-Schaaf mapping and the Birkhoff conjecture. [PDF]
PLoS ONE, 2018 The Ligon-Schaaf regularization (LS mapping) was introduced in 1976 and has been used several times. However, we are not aware of any direct usage of the inverse mapping, perhaps since it appears at first sight to be quite complex, involves the use of a ...
Thomas Sumner Ligon
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A novel binary Kepler optimization algorithm for 0–1 knapsack problems: Methods and applications
Alexandria Engineering Journal, 2023 The 0–1 Knapsack problem is a non-deterministic polynomial-time-hard combinatorial optimization problem that cannot be solved in reasonable time using traditional methods.
Mohamed Abdel-Basset +5 more
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Optimization of a photovoltaic/wind/battery energy-based microgrid in distribution network using machine learning and fuzzy multi-objective improved Kepler optimizer algorithms [PDF]
Scientific ReportsIn this study, a fuzzy multi-objective framework is performed for optimization of a hybrid microgrid (HMG) including photovoltaic (PV) and wind energy sources linked with battery energy storage (PV/WT/BES) in a 33-bus distribution network to minimize the
Fude Duan +5 more
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Symmetries and stability of motions in the Newtonian and the Hookean potentials [PDF]
Theoretical and Applied Mechanics, 2022 A new way of looking at symmetries is proposed, especially regarding their role in the stability of two-body motions in the Newtonian and the Hookean potentials, the two selected by Bertrand’s theorem. The role of the number of spatial dimensions is also
Carimalo Christian
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Proficient trigonometrical-fitted two-derivative multistep collocation methods in predictor-corrector approach: Application to perturbed Kepler problem. [PDF]
MethodsXLee KC, Aris MNM, Hashim I, Senu N.
europepmc +2 more sources
Elementary Solution of Kepler Problem (and a few other problems)
Revista Brasileira de Ensino de Física, 2022 We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force.
M. Moriconi
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Mathematics, 2022 The central problem of this study is to represent any holomorphic and square integrable function on the Kepler manifold in the series form based on Fourier analysis.
Zeyuan Song, Zuoren Sun
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On the Periodic Orbits of the Perturbed Two- and Three-Body Problems
Galaxies, 2023 In this work, a perturbed system of the restricted three-body problem is derived when the perturbation forces are conservative alongside the corresponding mean motion of two primaries bodies.
Elbaz I. Abouelmagd +2 more
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exoMMR: A New Python Package to Confirm and Characterize Mean Motion Resonances
The Astronomical Journal, 2023 The study of orbital resonances allows for the constraint of planetary properties of compact systems. We can predict a system’s resonances by observing the orbital periods of the planets, as planets in or near mean motion resonance (MMR) have period ...
Mariah G. MacDonald +4 more
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