LINEAR PHASE PORTRAITS: MATRIX ENTRY

The graphing window at right displays a few trajectories of the linear system \(\dot{x} = Ax\). Below the window the name of the phase portrait is displayed. Depress the mousekey over the graphing window to display a trajectory through that point. The trajectory can be dragged by moving the cursor with the mousekey depressed. Releasing it will leave the trajectory in place. Click on [Clear] to clear all the trajectories.

Choose between a companion matrix or a general matrix using the [Companion matrix] key.

Set the matrix entries by means of the sliders at bottom right. When [Companion Matrix] is selected, only the entries from the bottom row can be varied. In this case, the matrix can also be controlled by rolling over the plane at upper left or by grabbing the \([tr]\) or \([det]\) sliders alongside it.

Click the [eigenvalues] key to toggle display of a complex plane with the eigenvalues of A displayed and a readout of the eigenvalues.

© 2001 H. Hohn and H. Miller