![[double pendulum]](dbl_pend.gif)
Several examples are given below and short movies have been made of a specific computed trajectory.
Also, two students from the 1996 summer program working with Bob Thurman and Patrick Worfolk (postdocs at the Geometry Center) worked on computing and visualizing halo orbits and their stable and unstable manifolds for the restricted three body problem.
A double pendulum is one pendulum hung from a second pendulum.
Initial angular velocities are given, but then the pendulum
swings freely under the influence of gravity. The resulting
dynamics can be quite remarkable. One trajectory may be viewed as
an mpeg movie (360K).
![[3 bodies]](restrict3.gif)
The restricted three body problem is a model for the motion of a spacecraft
moving under the gravitational influence of two larger bodies which
are prescribing circular orbits around each other. For example, this
models a spacecraft in the earth-moon system; or a body moving in the
Sun-Jupiter system. A short mpeg movie (90K)
is available which shows one particular orbit in such a system.
![[surface]](surface.gif)
Finite dimensional dynamical systems are often used to approximate
PDE problems for the evolution of some sort of surface or interface.
Here we demonstrate in an mpeg movie (385K) a
simulation of the motion of such a surface whose motion is
specified by a 2-dimensional dynamical system.