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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
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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

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References

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