Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T14:11:38.407Z Has data issue: false hasContentIssue false
  • English
  • Français

The calculation of transients in dynamical systems

Published online by Cambridge University Press:  24 October 2008

E. E. Ward
E. E. Ward
Affiliation:
Electrical Engineering Department the University Birmingham, 15
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper shows that the calculation of transients by Tricomi's method using Laguerre functions is a practical alternative to the use of partial fractions. By taking numerical examples of Laplace transforms ranging from quadratic to sixth-power polynomials it shows that the approximation offered by this method would be acceptable for many practical uses. It analyses the composition of the coefficients of the Laguerre series, thus disclosing the conditions for quick convergence; for some transforms these conditions are not attainable.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 1 , January 1954 , pp. 49 - 59
Copyright
Copyright © Cambridge Philosophical Society 1954

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Aigrain, P. R. and Williams, E. M.The design of optimum transient response amplifiers. Proc. Inst. Radio Engrs, N.Y., 37 (1949), 873.Google Scholar
(2)Courant, R. and Hilbert, D.Methoden der Mathematischen Physik, 1 (Berlin, 1931).CrossRefGoogle Scholar
(3)Doetsch, G.Theorieund Anwendung der Laplace Transformation (Berlin, 1937), pp. 136, 181.CrossRefGoogle Scholar
(4)Jahnke, and Emde, F.Tables of Higher Functions (Leipzig, 1948), pp. 32, 33.Google Scholar
(5)Marden, M.The Geometry of the Zeros of a Polynomial (Amer. Math. Soc. Math. Surveys, no. 3, 1949), pp. 95 et seq.Google Scholar
(6)Picone, M.Sulla trasformata di Laplace. R.C. Accad. Lincei, Ser. 6, 21 (1935), 306.Google Scholar
(7)Tricomi, F.Trasformazione di Laplace e polinomi di Laguerre. I. R.C. Accad. Lincei, Ser. 6, 21 (1935), 235, para. 3.Google Scholar
(8)Wagner, K. W.Operatorenrechnung (Leipzig, 1940), p. 48.Google Scholar