Results 21 to 30 of about 11,157,685 (225)
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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ALGEBRAIC DESCRIPTION OF SHAPE INVARIANCE REVISITED
Acta Polytechnica, 2017 We revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical space, the Kepler problem in ...
Satoshi Ohya
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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
Mathematics, 2022 In this study, we consider eight stages per step family of explicit Runge-Kutta-Nyström pairs of orders eight and six. The pairs from this family effectively use eight stages for each step.
Houssem Jerbi +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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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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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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The Finsler geometry of the rotating Kepler problem
, 2014 Kai Cieliebak +2 more
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Revisiting Kepler: new symmetries of an old problem
Arnold Mathematical Journal, 2021 The Kepler orbits form a 3-parameter family of unparametrized plane curves, consisting of all conics sharing a focus at a fixed point. We study the geometry and symmetry properties of this family, as well as natural 2-parameter subfamilies, such as those
Gil Bor, Connor Jackman
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