Paper Info
Title
Planetary Motion and the Duality of Force Laws.
Abstract
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 $z \rightarrow z^2$. 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.
Year
DOI
Venue
2000
10.1137/S0036144598346005
SIAM Review
Keywords
Field
DocType
centripetal attraction,undergraduate complex analysis class,complex plane,two-body problem,force laws,general pair,geometric analysis,geometric function theory,planetary motion,conic section,functions of a complex variable,numerical study,power law,matlab program,distance travel,two body problem
Newton's law of universal gravitation,Hooke's law,Geometric function theory,Centripetal force,Mathematical analysis,Complex plane,Duality (optimization),Ellipse,Conic section,Law,Classical mechanics,Mathematics
Journal
Volume
Issue
ISSN
42
1
0036-1445
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Rachel W. Hall121.29
Kresimir Josic212316.63