Difference between revisions of "Hénon-Heiles System"
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| − | The Hénon-Heiles equation is a nonlinear nonintegrable [[Hamiltonian system]] where the potential energy function is defined by a [[ | + | The Hénon-Heiles equation is a nonlinear nonintegrable [[Hamiltonian system]] where the potential energy function is defined by a [[polar coordinate system]]. It was developed by [[Michel Hénon]] and [[Carl Heiles]] for modelling galactic dynamics. |
== Description == | == Description == | ||
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* [[Dynamical systems]] | * [[Dynamical systems]] | ||
* [[Hamiltonian system]] | * [[Hamiltonian system]] | ||
| + | * [[Polar coordinate system]] | ||
== External links == | == External links == | ||
Revision as of 07:38, 14 October 2016
The Hénon-Heiles equation is a nonlinear nonintegrable Hamiltonian system where the potential energy function is defined by a polar coordinate system. It was developed by Michel Hénon and Carl Heiles for modelling galactic dynamics.
Description
While at Princeton in 1962, Hénon and Heiles worked on the non-linear motion of a star around a galactic center where the motion is restricted to a plane.
In 1964 they have published an article titled 'The applicability of the third integral of motion: Some numerical experiments'.
Their original idea was to find a third integral of motion in a galactic dynamics. For that purpose they have taken a simplified two-dimensional nonlinear axi-symmetric potential and found that the third integral exist only for a limited number of initial conditions.
In the modern perspective these initial conditions which doesn't have the third integral motion are called chaotic orbits.
See also
External links
- Hénon-Heiles System @ Wikipedia
