General Theory of Optimal Rocket Trajectories

  • James M. Longuski
  • José J. Guzmán
  • John E. Prussing
Chapter
Part of the Space Technology Library book series (SPTL, volume 32)

Abstract

In this chapter we develop a general theory of optimal spacecraft trajectories based on two pioneering works: Breakwell [1959] and Lawden [1963]. Lawden introduced the concept of the primer vector, which plays a dominant role in minimum-propellant trajectories and also in other types of optimal trajectories. A more complete discussion of the topics in this chapter, including several example trajectories, is in Prussing [2010].

Keywords

Burning 

References

  1. J.V. Breakwell, The optimization of trajectories. J. Soc. Ind. Appl. Math. 7(2), 215–247 (1959)MathSciNetCrossRefMATHGoogle Scholar
  2. D.F. Lawden, Optimal Trajectories for Space Navigation (Butterworths, London, 1963)MATHGoogle Scholar
  3. G. Leitmann, On a class of variational problems in rocket flight. J. Aerosp. Sci. 26(9), 586–591 (1959)MathSciNetCrossRefMATHGoogle Scholar
  4. P.M. Lion, M. Handelsman, Primer vector on fixed-time impulsive trajectories. AIAA J. 6(1), 127–132 (1968)CrossRefMATHGoogle Scholar
  5. J.P. Marec, Optimal Space Trajectories (Elsevier Scientific, New York, 1979)MATHGoogle Scholar
  6. J.E. Prussing, Optimal impulsive linear systems: sufficient conditions and maximum number of impulses. J. Astronaut. Sci. 43(2), 195–206 (1995)MathSciNetGoogle Scholar
  7. J.E. Prussing, Chapter 2: primer vector theory and applications, in Spacecraft Trajectory Optimization, ed. by B.A. Conway (Cambridge University Press, New York, 2010)Google Scholar
  8. J.E. Prussing, B.A. Conway, Orbital Mechanics, 2nd edn. (Oxford University Press, New York, 2013)Google Scholar
  9. J.E. Prussing, S.L. Sandrik, Second-order necessary conditions and sufficient conditions applied to continuous-thrust trajectories. J. Guid. Control Dyn. (Engineering Note) 28(4), 812–816 (2005)Google Scholar

Copyright information

© Springer Science + Business Media New York 2014

Authors and Affiliations

  • James M. Longuski
    • 1
  • José J. Guzmán
    • 2
  • John E. Prussing
    • 3
  1. 1.Purdue UniversityLafayetteUSA
  2. 2.Orbital Sciences CorporationChantillyUSA
  3. 3.University of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations