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|a (JST)2653383
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|a eng
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|a Hall, Rachel W.
|e verfasserin
|4 aut
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|a Planetary Motion and the Duality of Force Laws
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|c 2000
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|a Text
|b txt
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|a Trajectories of Hooke's law in the complex plane, which are conic sections, are mapped onto trajectories of Newton's law of gravitation via the transformation z → z<sup>2</sup>. Newton's law of ellipses (objects attracted to a center by a force inversely proportional to the square of the distance travel in conic sections) follows from a geometric analysis of this map. An extension of this approach reveals a similar relation between more general pairs of power laws of centripetal attraction. The implications of these relations are discussed and a Matlab program is provided for their numerical study. This material is suitable for an undergraduate complex analysis class.
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|a Copyright 2000 Society for Industrial and Applied Mathematics
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|a Two-Body Problem
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|a Functions of a Complex Variable
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|a Geometric Function Theory
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|a S0036144598346005
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|a Physical sciences
|x Physics
|x Thermodynamics
|x Thermodynamic theory
|x Newtons law of cooling
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|a Philosophy
|x Logic
|x Logical topics
|x Formal logic
|x Mathematical logic
|x Mathematical duality
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|a Physical sciences
|x Physics
|x Mechanics
|x Classical mechanics
|x Kinematics
|x Trajectories
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|a Physical sciences
|x Physics
|x Mechanics
|x Classical mechanics
|x Hookes law
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|a Mathematics
|x Pure mathematics
|x Geometry
|x Geometric shapes
|x Conic sections
|x Ellipses
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|a Physical sciences
|x Physics
|x Mechanics
|x Classical mechanics
|x Kinetics
|x Laws of Motion
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Power laws
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|a Physical sciences
|x Astronomy
|x Astrophysics
|x Celestial mechanics
|x Orbits
|x Solar orbits
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|a Mathematics
|x Mathematical expressions
|x Mathematical theorems
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|a Physical sciences
|x Astronomy
|x Astrophysics
|x Celestial mechanics
|x Orbits
|x Planetary orbits
|x Education
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|a research-article
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|a Josic, Kresimir
|e verfasserin
|4 aut
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|i Enthalten in
|t SIAM Review
|d Society for Industrial and Applied Mathematics, 1959
|g 42(2000), 1, Seite 115-124
|w (DE-627)266886140
|w (DE-600)1468482-2
|x 10957200
|7 nnns
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|g volume:42
|g year:2000
|g number:1
|g pages:115-124
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|u https://www.jstor.org/stable/2653383
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|d 42
|j 2000
|e 1
|h 115-124
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