DiffEq Phase Plane Support Notes
DiffEq PhasePlane is one of the dynamical systems exploration tools in MacMath
9.2. MacMath 9.2 was developed
locally by Professor John Hubbard and Beverly West, and has been commerically
sold by Springer Verlag.
It specializes in exploring two dimensional autonomous systems of differential
equations dx/dt=f(x,y), dy/dt=g(x,y).
Related programs include DiffEq and DiffEq,
3D Views which specialize respectively
in the one and three dimensional cases.
The program Planar Systems in MacMath 9.6 is an incomplete
update
of DiffEq, Phase Plane, with
many nice additional features but at times incomplete support for basics like
printing.
Basic Operation
of the program involves entering a system of equations and then
clicking at various locations to
see the trajectories going through those points. By default trajectories
first continue forward until a window
boundary is encountered. Then a trajectory backwards (negative
time) from the initial point is traced. Clicking
the mouse while a trajectory segment is being traversed terminates
that direction of traversal immediately.
DiffEq Phase Plane gives very rich graphical displays but has no support for providing large amounts of numerical data.
The default stepsize is too large, often producing very jagged pictures.
So stepsize should generally be reduced from under the Change menu.
Some Frequently Asked Questions
-
Axes and Tickmarks
-
are added from the Settings menu.
-
Equations
-
are also changed from below the Change menu.
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Numerical Integration
-
methods available under the Change menu are Euler, Heun (midpoint
Euler) , and Runge-Kutta.
-
Rescaling
-
operations may require a carriage return to take effect.
-
Slope Marks
-
are available from the Settings menu. The program Planar Systems
is notable for improving the algorithm used in drawing these.
-
Step Sizes
-
by default are very large because the program was written many years ago.
Choose something smaller from below the Change menu.
-
Special Functions Supported include
-
Option-p for pi.
-
abs(), sqrt(), sgn(), ln(), exp(), atan(),
and floor().
-
^ is exponentiation.
-
Zooming
-
is accomplished by selecting Blow Up fromt the Task menu
and then selecting a rectangle while holding down the mouse button.
-
Equilibrium Points
-
can be found by selecting Locate Singularity from the Tasks
menu and then clicking to set a starting point for the search.
Location
In the folder MacMath 9.2 toplevel on all Macintoshes in the lab.
Printing
Most MacMath programs have some difficulty printing in the lab. Screen
Dumps should always be viewed
as the backup technique when difficulties are encountered. Turning
background printing off may also help
this program.
Documentation
A manual (yellow) for MacMath 9.2 is available in the lab bookcase.
Last Update: March 16, 1999