Results 31 to 40 of about 11,457,962 (286)
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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On the Proper Treatment of Dynamics in Cognitive Science
Topics in Cognitive Science, EarlyView., 2023 Abstract This essay examines the relevance of dynamical ideas for cognitive science. On its own, the mere mathematical idea of a dynamical system is too weak to serve as a scientific theory of anything, and dynamical approaches within cognitive science are too rich and varied to be subsumed under a single “dynamical hypothesis.” Instead, after first ...
Randall D. Beer
wiley +1 more source
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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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. Tsiganov
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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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Runge–Kutta Pairs of Orders 5(4) Trained to Best Address Keplerian Type Orbits
Mathematics, 2021 The derivation of Runge–Kutta pairs of orders five and four that effectively uses six stages per step is considered. The coefficients provided by such a method are 27 and have to satisfy a system of 25 nonlinear equations.
Vladislav N. Kovalnogov +4 more
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A novel hybrid algorithm of GSA with Kepler algorithm for numerical optimization
Journal of King Saud University: Computer and Information Sciences, 2015 It is now well recognized that pure algorithms can be promisingly improved by hybridization with other techniques. One of the relatively new metaheuristic algorithms is Gravitational Search Algorithm (GSA) which is based on the Newton laws. In this paper,
Soroor Sarafrazi +2 more
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An Index Theory for Zero Energy Solutions of the Planar Anisotropic Kepler Problem [PDF]
Communications in Mathematical Physics, 2017 In the variational study of singular Lagrange systems, the zero energy solutions play an important role. The anisotropic Kepler problem is such a singular system introduced by physicist M.
Xijun Hu, Guowei Yu
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Noether symmetries and integrability in time-dependent Hamiltonian mechanics [PDF]
Theoretical and Applied Mechanics, 2016 We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaré-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms.
Jovanović Božidar
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Etudes Epistémè, 2023 Harmony of the spheres is an important chapter in musical theory, as in Marin Mersenne. In the Traité de l’harmonie universelle (1627), the philosopher makes an inventory of the problem for pedagogical purposes.
Julien Gominet-Brun
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