Matrix analysis of linear conservative systems

✍ Scribed by Louis A. Pipes

• Publisher: Elsevier Science
• Year: 1962
• Tongue: English
• Weight: 511 KB
• Volume: 274
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(62)90830-x

✦ Synopsis

The loop differential equations of any lossless, reciprocal electric circuit are integrated by the use of functions of matrices. It is shown how the transient analysis of such circuits is a generalization of the analysis of the simple single-loop circuit composed of a linear inductance in series with a linear elastance. The scaler trigonometric functions that appear in the analysis of the single-loop circuit are replaced by matric trigonometric functions in the analysis of the general circuit of n loops. The matric functions are then expanded by a form of Sylvester's theorem. The case in which the circuit has multiple eigenvalues is particularly easy to analyze by the use of functions of matrices. The analysis is extended to the forced oscillations of the n-loop linear conservative circuit.

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