Eigenvalue Analysis

Eigenvalue Analysis

A lot of information about the intrinsic behavior of the system is available by computing the eigenvalues of the Jacobian matrix (matrix A). Note that for this, you do not need to have any control or observer variables, but you must have some free states.

Procedure

1. Select Eigenvalues from the Linear analysis menu to see the result, after the run is complete.

Figure 64: Eigenvalues analysis dialog box

It is not difficult to work out the eigenvalues of this system analytically which is consistent with these results. 1000 is the ratio between the spring stiffness (100 000 N/m) and the mass (100 kg) in SI units.

2. In the Linearization time field, select the different times in turn.

The eigenvalues table is then updated in the Linear Analysis - Eigenvalues box to show the eigenvalues of the associated A matrix. You will find that the eigenvalues are always the same for each .jac file. You can sort the eigenvalues according to their real part, imaginary part, frequency or their damping ratio by clicking on the title of the appropriate column. By default, they are sorted in ascending order of frequency in Hz.

3. To store the current list of eigenvalues in a file, select Save.

The .jac files are ASCII text files and can be examined in an editor and printed to see the elements of the A matrix.