Hostname: page-component-7bb8b95d7b-s9k8s Total loading time: 0 Render date: 2024-09-12T22:14:47.139Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

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. Hohmann, W. Die Erreichbarkeit der Himmelskörper, Oldenburg, Munich, 1925.Google Scholar
2. Hoelker, R. F. and Silber, R. The Bi-Elliptical Transfer Between Circular Coplanar Orbits. Army Ballistic Missile Agency, Redstone Arsenal, Alabama, Report No. DA-TM-2-59, 1959.Google Scholar
3. Lawden, D. F. Mathematical Problems of Astronautics. Mathematical Gazette, Vol. 41, No. 337, p. 168, 1957.Google Scholar
4. Ewing, G. M. A Fundamental Problem of Navigation in Free Space. Quarterly of Applied Mathematics, Vol. 18, No. 4, p. 355, 1961.Google Scholar
5. Lawden, D. F. Minimal Rocket Trajectories. Journal of the American Rocket Society, Vol. 23, No. 6, p.360, 1953.Google Scholar
6. Lawden, D. F. Fundamentals of Space Navigation. Journal of the British Interplanetary Society, Vol. 13, No. 2, p. 87, 1954.Google Scholar
7. Cicala, P. Le Evoluzioni Ottime di un Aereo. Accademia delle Scienze di Torino. Classe di Scienze Fisiche Matamatiche e Naturali, Vol. 89, p. 350, 1954-5.Google Scholar
8. Bliss, G. A. Lectures on the Calculus of Variations, Chapter 7. University of Chicago Press, 1946.Google Scholar
9. Lawden, D. F. Interplanetary Rocket Trajectories. Advances in Space Science, Vol. 1, Chapter 1, Academic Press, New York, 1959.Google Scholar
10. Lawden, D. F. Necessary Conditions for Optimal Rocket Trajectories. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 12, Part 4, p. 476, 1959.Google Scholar
11. Miele, A. General Variational Theory of the Flight Paths of Rocket-Powered Aircraft, Missiles and Satellite Carriers. Astronautica Acta, Vol.4, Part 4, p. 264, 1958.Google Scholar
12. Lawden, D. F. Optimal Intermediate-Thrust Arcs in a Gravitational Field. Astronautica Acta, Vol. 8, No. 2, p. 106, 1962.Google Scholar
13. Leitmann, G. On a Class of Variational Problems in Rocket Flight. Journal of the Aero/Space Sciences, Vol. 26, No. 9, p. 586, 1959.Google Scholar
14. Lawden, D. F. Impulsive Transfer Between Elliptical Orbits. Optimisation Techniques, Chapter 11, Academic Press, New York, 1962.Google Scholar
15. Bender, D. F. Optimum Co-planar Two Impulse Transfers Between Elliptic Orbits. Institute of Aerospace Sciences Preprint 62-4, 1962.Google Scholar