Hénon-Heiles equation
Encyclopedia
The Henon-Heiles equation is used to model star
s. It is expressed as
While at Princeton
in 1964, Michel Hénon
and Carl Heiles published a paper that describes the non-linear motion of a star around a galactic center where the motion is restricted to a plane.
The Henon-Heiles System (HHS) is defined by the following four equations:
where
and 
. Since HHS is specified in 
, we need a Hamiltonian of degrees of freedom two to model it.
It can be solved for some cases using Painleve Analysis.
The Hamiltonian for the HHS is
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s. It is expressed as
While at Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1964, Michel Hénon
Michel Hénon
Michel Hénon is a mathematician and astronomer. He is currently at the Nice Observatory.In astronomy, Hénon is well known for his contributions to stellar dynamics. In late 1960s and early 1970s he was involved in dynamical evolution of star clusters, in particular the globular clusters...
and Carl Heiles published a paper that describes the non-linear motion of a star around a galactic center where the motion is restricted to a plane.
The Henon-Heiles System (HHS) is defined by the following four equations:
where
and . Since HHS is specified in , we need a Hamiltonian of degrees of freedom two to model it.It can be solved for some cases using Painleve Analysis.
The Hamiltonian for the HHS is