DsTool Help Page

What is DsTool?

DsTool (short for Dynamical Systems TOOLkit) is a public-domain software package for researchers and educators studying dynamical systems (both differential equations and discrete time systems). It provides the user with an interactive graphical interface for computations in dynamical systems and visualization of resulting geometric structures.

DsTool runs on both the SUN and SGI/IRIS workstations at the Geometry Center.

How to quit DsTool

To quit DsTool,

Locate the Command Panel (the long, short, window titled "DsTool: version #..."))
Hold down the left mouse button on the "File" menu item
Drag the cursor down to the menu item labeled "Exit"

Helpful hint

Whenever the expression "press the button marked..." is used in this document, it means "move the mouse so that the cursor is pointing to the button marked.... Then click the left mouse button."

Computing a trajectory

The largest window in DsTool is called the Two-D View Window. This is where trajectories are displayed.

You can initiate the computation of a trajectory forward in time in two ways:

From the Orbits Panel
- Click the left mouse button on the panel item Forwards.
- The initial conditions for the trajectory are taken from those in the text fields of the Initial column in the Selected Point Panel.
- Edit the initial conditions by pressing the left mouse button in the Initial field and using keyboard input.
By using the mouse
- Press the left mouse button near the center of the Two-D View Window to select an initial condition.
- Click the middle mouse button to start the computation of a trajectory.

A trajectory can be continued from the last point calculated by

Pressing the middle mouse button in the view window; OR
Clicking the left mouse button on the Continue button of the Orbits Panel.

Trajectory calculations can be initiated in backwards time by

Pressing the left mouse button on the Backwards button of the Orbits Panel; OR
Pressing the right mouse button near the center of the Two-D View Window to select an initial condition, and then the middle mouse button to begin computation of the trajectory.

Stopping when an event occurs

Sometimes you want to compute a trajectory until a certain event occurs. For this example, we will assume that you want to stop a trajectory every time that the velocity, v, of a particle is zero. That is, we want to stop whenever v=0.

On the Orbits Panel, find the menu item labeled Stopping Condition.
By holding down the left mouse button, produce a menu of options.
Drag the cursor down to the second menu item: Event Stopping, and release the left mouse button.
A list of entries at the botton of the Orbits Panel is now active. Type a 0 on the input field next to the label v.
Click the button to the right of this field.
Now the trajectory will stop every time the variable v passes through the value 0.

To return to the default stopping mode,

On the Orbits Panel, find the menu item labeled Stopping Condition.
By holding down the left mouse button, produce a menu of options.
Drag the cursor down to the second menu item: Fixed Steps, and release the left mouse button.

Clearing old data

When the screen becomes cluttered, you can erase the plotted trajectories by pressing the Clear button in the Two-D View panel.

Zooming in and out

Sometimes you may want to change the range of the window in which trajectories are displayed. This can be done in two ways:

by editing the text fields Min: and Max: at the top of the Two-D View Window. You will then need to refresh the screen. OR
by mousing action
- Hold down the left mouse button in the Two-D View Window, and drag the mouse to draw a "rubber band rectangle."
- When the left mouse button is released, a pop-up panel appears.
- If Zoom in is selected, the area inside the rectangle is rescaled to the plotting window.
- If Zoom out is selected, the plotting window is rescaled so that the view window becomes the area inside the rectangle.

After zooming in or out you may want to return the viewing range of the TwoD View Window to its default values. To do this, click on the button marked Reset to default range at the bottom of the Two-D View Window.

How to refresh the screen

After changing the view ranges of the Two-D View Window (and at other times) you will want to redraw previously computed trajectories. To do this, click on the Refresh button at the bottom of the Two-D View Window.

How to change models

To select a new dynamical system:

Hold down the left mouse button on the field labeled Models on the Command panel.
Drag the pointer down the pop-up menu to select a category you want (for example, Vector Fields).
Select the dynamical system of interest from the second level of pop-up menus that appear to the right of each category.

How to load a data file

To load a file into DsTool:

Locate the Command Panel.
Hold down the left mouse button button labeled File.
Drag the pointer down the pop-up menu to select the Load entry.
When the Load Panel pops up, enter the full name of the directory and filename that you want to load. For example, if you want to load the file mydata.dstool in the directory /u/mydirectory you would enter /u/mydirectory in the field that asks for the directory name, and you would type mydata.dstool in the "Filename" field.
Press the Load button.

The Main (Command) Panel

The Command Panel is used to change models and to call up other DsTool panels and features. For easy identification, here is a picture of the Command Panel.

The Selected Point Panel

The Selected Point Panel is used to type in initial conditions for a dynamical system. For easy identification, here is a picture of the Selected Point Panel.

The Orbits Panel

The Orbits Panel is used to control the computation of the trajectory of a dynamical system. For easy identification, here is a picture of the Orbits Panel.

The 2D View Panel

The 2D View Panel is used to display the computed trajectories for the dynamical system being studied. For easy identification, here is a picture of the 2D View Panel.

Robert E. Thurman <thurman@geom.umn.edu>

Last modified: Mon Nov 25 16:16:14 1996