<story><title>Planar Choreographies: odd orbital mechanics</title><url>http://www.maths.manchester.ac.uk/~jm/Choreographies/</url></story><parent_chain></parent_chain><comment><author>ColinWright</author><text>The paper is here: &lt;a href=&quot;http://arxiv.org/abs/1305.0470&quot; rel=&quot;nofollow&quot;&gt;http://arxiv.org/abs/1305.0470&lt;/a&gt;&lt;p&gt;&lt;pre&gt;&lt;code&gt;    Classification of symmetry groups for planar n-body choreographies
    James Montaldi, Katrina Steckles
    (Submitted on 2 May 2013)

    Since the foundational work of Chenciner and Montgomery in 2000 there
    has been a great deal of interest in choreographic solutions of the
    n-body problem: periodic motions where the n bodies all follow one
    another at regular intervals along a closed path. The principal approach
    combines variational methods with symmetry properties. In this paper, we
    give a systematic treatment of the symmetry aspect. In the first part we
    classify all possible symmetry groups of planar n-body, collision-free
    choreographies. These symmetry groups fall in to 2 infinite families and,
    if n is odd, three exceptional groups. In the second part we develop the
    equivariant fundamental group and use it to determine the topology of the
    space of loops with a given symmetry, which we show is related to certain
    cosets of the pure braid group in the full braid group, and to centralizers
    of elements of the corresponding coset.&lt;/code&gt;&lt;/pre&gt;</text></comment>
<story><title>Planar Choreographies: odd orbital mechanics</title><url>http://www.maths.manchester.ac.uk/~jm/Choreographies/</url></story><parent_chain></parent_chain><comment><author>VLM</author><text>That&apos;s cool, and attractive, and visually appealing.&lt;p&gt;I do have a request.  Look at stuff like &quot;Belbruno Orbits&quot; &quot;Low energy transfer orbits&quot; &quot;ITN Interplanetary Transport Network&quot;.  Then look at the nice clean easy to use visualizer we&apos;re linked to.  Then do the obvious merger of the two...&lt;p&gt;Yes I already know there&apos;s a way to visualize Belbruno orbits with ORSA or other full fledged simulation packages, but its not quite as easy and convenient as this webpage.&lt;p&gt;You know what would make an interesting web standard or maybe startup idea?  A universal internet standard free dynamics system.  Not just for orbits but even physics 101 basic kinematics.  Think of like the animated drawing blueprints on &quot;Mythbusters&quot; but simply include a javascript package of some type (or whatever) and then the end user merely provides three things:  enumerated list of URL for sprite graphics, starting conditions for those objects both simple coordinates and maybe &quot;hidden&quot; variables, and the math equation(s) governing.  Not general purpose &quot;here&apos;s mathematica in node.js&quot; just dynamics.</text></comment>