Results 11 to 20 of about 11,157,685 (225)
The dynamics of the relativistic Kepler problem
Results in Physics, 2020 We deal with the Hamiltonian system (HS) associated to the Hamiltonian in polar coordinates H=12pr2+pϕ2r2-1r-∊2r2, where ∊ is a small parameter. This Hamiltonain comes from the correction given by the special relativity to the motion of the two-body ...
Elbaz I. Abouelmagd +2 more
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Darboux Inversions of the Kepler Problem [PDF]
Regulârnaâ i haoticeskaâ dinamika, 2022 While extending a famous problem asked and solved by Bertrand in 1873, Darboux found in 1877 a family of abstract surfaces of revolution, each endowed with a force function, with the striking property that all the orbits are periodic on open sets of the ...
Alain Albouy, Lei Zhao
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The Kepler Problem: Polynomial Algebra of Nonpolynomial First Integrals [PDF]
Regulârnaâ i haoticeskaâ dinamika, 2019 The sum of elliptic integrals simultaneously determines orbits in the Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors is defined by ...
A. V. Tsiganov
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Periodic Solutions to a Perturbed Relativistic Kepler Problem [PDF]
SIAM Journal on Mathematical Analysis, 2020 We consider a perturbed relativistic Kepler problem \begin{equation*} \dfrac{\mathrm{d}}{\mathrm{d}t}\left(\dfrac{m\dot{x}}{\sqrt{1-|\dot{x}|^2/c^2}}\right)=-\alpha\, \dfrac{x}{|x|^3}+\varepsilon \, \nabla_x U(t,x), \qquad x \in \mathbb{R}^2 \setminus ...
A. Boscaggin +2 more
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Regularization of Kepler problem in κ-spacetime [PDF]
, 2016 In this paper, we regularize the Kepler problem on κ-spacetime in several different ways. First, we perform a Moser-type regularization and then we proceed for the Ligon-Schaaf regularization to our problem.
Partha Guha, E. Harikumar, N. S. Zuhair
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Mathematische Annalen, 2021 In this paper, we consider a time-periodically forced Kepler problem in any dimension, with an external force which we only assume to be regular in a neighborhood of the attractive center. We prove that there exist infinitely many periodic orbits in this
Lei Zhao
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Reduction and regularization of the Kepler problem
Celestial mechanics & dynamical astronomy, 2021 The KS regularization connects the dynamics of the harmonic oscillator to the dynamics of bounded Kepler orbits. Using orbit space reduction, it can be shown that reduced harmonic oscillator orbits can be identified with re-parametrized Kepler orbits by ...
J. C. Meer
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Periodic solutions and regularization of a Kepler problem with time-dependent perturbation [PDF]
Transactions of the American Mathematical Society, 2017 We consider a Kepler problem in dimension two or three, with a time-dependent $T$-periodic perturbation. We prove that for any prescribed positive integer $N$, there exist at least $N$ periodic solutions (with period $T$) as long as the perturbation is ...
A. Boscaggin, R. Ortega, Lei Zhao
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Hamiltonian structures for integrable hierarchies of Lagrangian PDEs [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this theory is not a Lagrange function but a differential $d$-form that is ...
Mats Vermeeren
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Runge–Kutta Pairs of Orders 6(5) with Coefficients Trained to Perform Best on Classical Orbits
Mathematics, 2021 We consider a family of explicit Runge–Kutta pairs of orders six and five without any additional property (reduced truncation errors, Hamiltonian preservation, symplecticness, etc.). This family offers five parameters that someone chooses freely.
Yu-Cheng Shen +3 more
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