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## Three-dimensional Plots

What does it do? When you must solve three simultaneous differential equations, then the phase portrait of the system is three dimensional. You may view it using this 3-d display.

How do I use it? The controls on this display differ considerably from those associated with 2-d plots. In particular, there are many views of the phase portrait in three dimensions, while in 2-d the only question is how much to zoom in. The idea behind the 3-d plot is that you, the observer, sit on a comfortable chair in space, and have the ability to fly around the orbits of the differential equation to view them from different angles and distances. You also have a camera with a zoom lens that allows you to determine the field of view with which you examine the orbits. Thus, one of the chief sets of controls for 3-d plots concerns the observer position and the focus of her view. In the display dialog box, you may choose the point in space from which you want to observe, and the point in space at which you want to look (called the focus). Finally, you may choose the field of view for the scene. The field of view is the maximum angle (in degrees) from the center point of the view you desire.

The mouse behaves differently for 3-d plots than for 2-d plots. You may no longer set initial conditions using the mouse. Instead, you use the mouse to manipulate the view.

• Clicking the left mouse button and moving the mouse from side to side causes your observer position to shift on a line of latitude.
• Moving the mouse up and down when the left button is down causes your observer position to shift on a line of longitude.
• Holding the right button down and moving the mouse upwards causes your observer position to move closer to the focus. Holding the right button down and moving the mouse downwards causes your observer position to move away from the focus.

As a result of the differences in the use of the mouse, you must use the initial conditions dialog box to set initial conditions. Moreover, you will need to use the button on the tool bar or the Compute Orbit item on the Orbits menu to draw the orbit.

What are the defaults? You receive the 3-d display as the default display when you type more than two differential equations into the equation dialog box. The default variables are the first three variables associated with differential equations. The default observer position is (15,15,10), while the initial focus is the origin. The default field of view is 20 degrees

Next: Example Up: Displays Previous: Example

Kevin Cooper
Wed Sep 30 15:21:52 PDT 1998