Terms in Control Theory

What are Eigenvalues ?

Eigenvalues are often introduced in the context of linear algebra or matrix theory. Historically, however, they arose in the study of quadratic forms and differential equations. Euler studied the rotational motion of a rigid body and discovered the importance of the principal axes. Lagrange realized that the principal axes are the eigenvectors of the inertia matrix.[11] In the early 19th century, Cauchy saw how their work could be used to classify the quadric surfaces, and generalized it to arbitrary dimensions.[12] Cauchy also coined the term racine caractéristique (characteristic root) for what is now called eigenvalue; his term survives in characteristic equation.

One of the particular values of a certain parameter for which a differential equation or matrix equation has an eigenfunction. In wave mechanics an eigenvalue is equivalent to the energy of a quantum state of a system

1. 1. 

   each of a set of values of a parameter for which a differential equation has a non-zero solution (an eigenfunction) under given conditions.
2. 2. 

   any number such that a given matrix minus that number times the identity matrix has zero determinan

What is Campbell Diagram & where is it used?

A Campbell diagram plot represents a system's response spectrum as a function of its oscillation regime. It is named for Wilfred Campbell, who introduced the concept., also called interference diagram.
In acoustical engineering, the Campbell diagram would represent the pressure spectrum waterfall plot vs the machine's shaft rotation speed.The campbell diagram is used to evaluate the critical speed at different operating speed.