An Analog Computer for the Solution of Eigenvalue Problems

Citation

Gleghorn, George Jay, Jr. (1955) An Analog Computer for the Solution of Eigenvalue Problems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FK46-6J12. https://resolver.caltech.edu/CaltechETD:etd-12152003-110324

Abstract

This thesis describes a computer suitable for the determination of the eigenvalues and eigenvectors of conservative mechanical and electrical systems. In essence, the computer consists of several active circuits with input impedances which act as negative resistances at the operating frequency of the computer. These negative resistances are interconnected with passive resistors and transformers to form a circuit analogous to the system being studied. For any setting of the control the analog represents the original system at a single frequency only, consequently it cannot be used for transient analysis. It is shown that the analog circuit is, in general, unstable at the control settings that are of interest, but that the application of suitable constraints suppresses the oscillations so that measurements may be made. The negative resistance circuits are designed so that parasitic impedances have little effect on the results. The computer has been found to produce results accurate to one per cent in most cases.

Thesis Files