Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T16:22:07.832Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Trajectories and the Accessory Minimum Problem

Published online by Cambridge University Press:  07 June 2016

D. J. Bell
D. J. Bell*
Affiliation:
Bristol College of Science and Technology
Get access

Summary

The necessary conditions of Clebsch and Weierstrass and of the multiplier rule in the calculus of variations, which arise from the study of the first variation of a function, are summarised. A further necessary condition associated with the second variation is stated. The latter condition is applied to two problems: (i) the determination of the thrust-time programme which maximises the altitude of a sounding rocket, (ii) the determination of the thrust direction programme for a rocket with a known propellant expenditure programme which yields a maximum range. In both problems it is found that the additional necessary condition is satisfied.

Type
Research Article
Information
Aeronautical Quarterly , Volume 16 , Issue 3 , August 1965 , pp. 205 - 220
Copyright
Copyright © Royal Aeronautical Society. 1965

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

1. Bliss, G. A. Lectures on the Calculus of Variations. University of Chicago Press, 1946.Google Scholar
2. Miele, A. The Calculus of Variations in Applied Aerodynamics and Flight Mechanics, Chap. 4, p. 128 of Optimization Techniques with Applications to Aerospace Systems, Leitmann, G. (Editor). Academic Press, London, 1962.Google Scholar
3. Lawden, D. F. Optimal Trajectories for Space Navigation, Chap. 2, p. 32. Butterworth, London, 1963.Google Scholar
4. Kelley, H. J. Guidance Theory and Extremal Fields. Transactions of the Institute of Radio Engineers, Professional Group Automatic Control, p. 75, 1962.Google Scholar
5. Kelley, H. J., Kopp, R. and Moyer, R. A Successive Optimization Procedure Using the Second Variation. American Institute of Aeronautics and Astronautics Conference on Astronautics, Yale University, August 1963.Google Scholar
6. Cavoti, C. R. Necessary and Sufficient Conditions for an Optimum in a Class of Flight Trajectories. Zeitschrift für Flugwissenschaften, Vol. II, Chap. 12, p. 485, 1963.Google Scholar