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Analytical Techniques for the Optimisation of Rocket Trajectories

Published online by Cambridge University Press:  07 June 2016

Derek F. Lawden
Derek F. Lawden*
Affiliation:
University of Canterbury, New Zealand
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Summary

The development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.

Type
Research Article
Information
Aeronautical Quarterly , Volume 14 , Issue 2 , May 1963 , pp. 105 - 124
Copyright
Copyright © Royal Aeronautical Society. 1963

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