Page 359 - Mechanical Engineers' Handbook (Volume 2)

350 Mathematical Models of Dynamic Physical Systems

Table 8 (Continued)

6.2 Eigenstructure
The internal structure of a system (and therefore its free response) is defined entirely by the
system matrix A. The concept of matrix eigenstructure, as defined by the eigenvalues and
eigenvectors of the system matrix, can provide a great deal of insight into the fundamental
behavior of a system. In particular, the system eigenvectors can be shown to define a special
set of first-order subsystems embedded within the system. These subsystems behave inde-
pendently of one another, a fact that greatly simplifies analysis.

System Eigenvalues and Eigenvectors
For a system with system matrix A, the system eigenvectors v and associated eigenvalues
i
are defined by the equation
i