# Dynamical systems: Simulation and visualization

One of the goals of the dynamical systems project at the Geometry
Center is an interface between the software package DsTool, for numerical simulation of dynamical
systems (created at the Center for Applied Mathematics, Cornell
University), and
Geomview, for visualization of geometric objects in 3 (and higher)
dimensions (created at the Geometry Center). This interface allows
one to see, as it is computed, a trajectory in configuration space of
the dynamical system being modelled.
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.

### The double pendulum

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).

### The restricted three body problem

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.

### An oscillating surface

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.

The DsTool software with an interface written in Tcl/Tk and
running on Unix workstations and PCs with linux is available from this site at Cornell:

http://www.math.cornell.edu/~gucken/software.html
See also Lloyd Wood's writeup about DsTool, with links to source, binaries, documentation etc. ...

http://personal.ee.surrey.ac.uk/Personal/L.Wood/software/DsTool/

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Last modified:
Thu Jun 1 10:08:36 CDT 2017