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| [[File:Henon heiles potential.svg|thumb|Contour plot of the Hénon-Heiles potential]] | | Jimmy is what his [http://browse.Deviantart.com/?q=spouse+loves spouse loves] to phone him while it is not his start identify. For many years he is been residing in Kentucky but he will have to transfer just one day or a further. He is actually fond of to engage in state songs and he's been executing it for rather a while. Invoicing is how he helps make a residing. He is running and [http://dict.leo.org/?search=protecting protecting] a blog in this article: http://wiki.jtu5.com/index.php?title=%E7%94%A8%E6%88%B7%3AMittieZZOQ<br><br>Here is my site ... [http://wiki.jtu5.com/index.php?title=%E7%94%A8%E6%88%B7%3AMittieZZOQ Mulberry piccadilly] |
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| The '''Hénon-Heiles equation''' is used to model [[star]]s. It is expressed as<ref>{{Citation
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| |first= Michel
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| |last= Hénon
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| |title= Chaotic Behaviour of Deterministic Systems
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| |chapter= Numerical exploration of Hamiltonian Systems
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| |pages= 53–170
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| |editor-first = G.
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| |editor-last= Iooss
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| |publisher= Elsevier Science Ltd
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| |year= 1983
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| |isbn= 044486542X
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| }}</ref>
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| :<math>
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| V(x,y) = \frac{1}{2}(x^2+y^2+2 x^2y - \frac{2}{3}y^3)
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| </math>
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| While at [[Princeton University|Princeton]] in 1962, [[Michel Hénon]] and [[Carl Heiles]] worked on the non-linear motion of a star around a galactic center where the motion is restricted to a plane. They published a paper<ref>{{cite journal
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| |author= Hénon, M.; Heiles, C.
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| |title= The applicability of the third integral of motion: Some numerical experiments
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| |journal= The Astrophysical Journal
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| |volume= 69
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| |pages= 73–79
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| |year= 1964
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| |bibcode= 1964AJ.....69...73H
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| |doi = 10.1086/109234 }}</ref>
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| that describes their work in 1964.
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| The Hénon-Heiles System (HHS) is defined by the following four equations:
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| :<math>
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| dx/dt=u
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| </math>
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| :<math> | |
| dy/dt=v
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| </math>
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| :<math> | |
| du/dt=-Ax-2xy
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| </math>
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| :<math>
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| dv/dt=-By+\epsilon y^2-x^2
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| </math>
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| where <math> A,B, \epsilon \in \R, A > 0</math> and <math>B > 0 </math>. Since HHS is specified in <math>\R^2</math>, we need a Hamiltonian of degrees of freedom two to model it.
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| It can be solved for some cases using Painlevé Analysis.
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| The Hamiltonian for the HHS is
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| :<math> H=\frac1 2 (u^2+v^2+Ax^2+By^2 )+x^2 y-\frac 1 3 \epsilon y^3</math>
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| == References ==
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| {{Reflist}}
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| == External links ==
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| * http://mathworld.wolfram.com/Henon-HeilesEquation.html
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| {{DEFAULTSORT:Henon-Heiles Equation}}
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| [[Category:Stellar astronomy]]
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