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A note on Smale's formulation of electrical network theory

Published online by Cambridge University Press:  24 October 2008

D. K. Arrowsmith  and
R. Smith
D. K. Arrowsmith
Affiliation:
Department of Mathematics, Westfield College, University of London, London, NW3 1ST
R. Smith
Affiliation:
Department of Mathematics, Leicester PolytechnicLeicester, LEI 9BH
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Extract

We consider in this note two problems which arise naturally in Smale's paper (3).

First of all we show that it is easy to extend Smale's results on the dynamics of LCR circuits with non-linear elements to circuits containing triode valves. It should be noted that transistors and other n-ports (1) can also be easily accommodated within this theory with suitable differentiability assumptions. We then further extend the theory to include elements whose voltage depends explicitly on time.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 3 , May 1976 , pp. 537 - 544
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

(1)Brayton, R. and Moser, J.A theory of non-linear networks, I, II. Quart. Appl. Math. 22 (1964), 1–33, 81–104.Google Scholar
(2)Lawden, D. F.Mathematics of engineering systems (Methuen, 1961).Google Scholar
(3)Smale, S.On the mathematical foundations of electrical network theory. J. Differential Geometry 7 (1972), 193–210.Google Scholar