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Some examples of the application of the Beecham-Titchener-Simpson (BTS) method to autonomous systems

Published online by Cambridge University Press:  04 July 2016

P. A. T. Christopher  and
R. Thorne
P. A. T. Christopher
Affiliation:
College of Aeronautics, Cranfield Institute of Technology, Cranfield, Bedford
R. Thorne
Affiliation:
College of Aeronautics, Cranfield Institute of Technology, Cranfield, Bedford
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Summary

It is noted that the averaging technique of Beecham and Titchener, for obtaining approximate solutions to nonlinear, ordinary, differential equations, is not widely known or used. In its extended form, as given by Simpson and Ross it appears to offer a unified and useful approach to the solution of many dynamical and other problems. The present paper sets out to describe and discuss, through the medium of a collection of examples, the Beecham-Titchener-Simpson (BTS) method in an effort to encourage its more widespread use.

Type
Research Article
Information
The Aeronautical Journal , Volume 89 , Issue 890 , December 1985 , pp. 380 - 402
Copyright
Copyright © Royal Aeronautical Society 1985 

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References

1. Minorsky, N. Non-linear oscillations, Van Nostrand, Princeton, NJ, 1962.Google Scholar
2. Nayfeh, A. H. Perturbation methods, John Wiley. New York, 1973.Google Scholar
3. Nayfeh, A. H. and Mook, D. T. Non-linear oscillations, John Wiley, 1979.Google Scholar
4. Beecham, L. J. and Titchener, I. M. Some notes on an approximate solution for the free oscillation characteristics of nonlinear systems typified by Aeronautical Research Council (UK) R and M 3674,1971.Google Scholar
5. Ross, A. J. and Beecham, L. J. An approximate analysis of the non-linear lateral motion of a slender aircraft (HP 115) at low speeds. ARC R and M 3674,1971.Google Scholar
6. Ross, A. J. Investigation of non-linear motion experienced on a slender-wing research aircraft. Journal of Aircraft. 1972, 9, No. 9,625–631.Google Scholar
7. Titchener, I. M. Non-linear dynamic-motion characteristics of a series of missile configurations from simulated flight behaviour at Mach numbers of 1-6 and 20 ARC R and M 3764,1975.Google Scholar
8. Ross, A. J. and Christopher, P. A. T. Approximate analytic methods for the solution ofaclassof strongly non-linear differential equations — a comparison. ARC R and M 3724,1973.Google Scholar
9. Simpson, A. An algorithm for autonomous non-linear dynamical equations. Aeronautical Quarterly, August 1977,211–234.Google Scholar
10. Titchener, I. M. Development of a technique for the analysis of non-linear dynamic characteristics of a flight vehicle. RAE Farnborough (UK) TR 73023,1973.Google Scholar
11. Butenin, N. Elements of the theory of non-linear oscillations. Blaisdel, New York, 1965.Google Scholar
12. Stoker, J. J. Non-linear vibrations. Interscience Publishers, New York, 1950.Google Scholar
13. Copson, E. T. Theory of functions of a complex variable. Oxford University Press, 1960.Google Scholar
14. Abramowitz, M. and Stegun, I. A. Handbook of mathematical functions, Dover Publications, New York, 1965.Google Scholar
15. Mclachlan, N. W. Bessel functions for engineers. Oxford University Press, 1948.Google Scholar
16. Hahn, w. Stability of Motion, Springer-Verlag, Berlin, 1967.Google Scholar
17. Hopkin, H. R. A scheme of notation and nomenclature for aircraft dynamics and associated aerodynamics. ARC R and M 3562,1966.Google Scholar
18. Thorne, R. Some experimental and theoretical studies in aircraft stability at high angles of attack. CJT Cranfield, College of Aeronautics, PhD Thesis, September, 1983.Google Scholar