Simó's simple 3body choreographies and their Fourier Transforms
Recently (to 3 December 2002, from my point of view) Carles Simó
has released a new set of 3body choreographies at http://www.maia.ub.es/dsg/3body.html
.
They are obviously candidates for taking the Geometrical Fourier
Transform. This page indexes the results of doing that. The technical
difficulties involved in doing it, using Mathematica and starting from a
large data file in a rather obscure GNUPlot format, are discussed elsewhere.
The files are just indexed with the numbering that Simo published them
in, 1–345. They are grouped into blocks just because there are so
many. The MooreChencinerMontgomery solution is number 001. The 000
case is the Lagrange equilateral triangle solution. This page has just
50 thumbnails, namely numbers 00–049. For more, up to number 345,
go to other blocks using the menu at the top of the page. Some of the
orbits Simó has found are amazingly complex for periodic orbits
with three equispaced (in time) bodies runnning around after each other.
Missing images suggest bugs in my processing or in my derived data
files. For an explanation of the notation and coloring of the diagrams
see the Guide under its button.
There are animated SVG forms of the
images available, if you have a newer browser and have already, or are
willing to, download the Adobe SVG
Viewer Plugin, or some other viewer. [SVG (Scalable Vector
Graphics) is a recommended XML
markup for twodimensional graphics coming from the W3C (World Wide Web Consortium), who bring
us HTML, HTTP, XML, PNG, CCS, MathML, RDF and many other protocols for
the Web.]
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