Advertisement

Variational problems in space flight mechanics

  • G. L. Grodzovsky
Contributed Papers

Abstract

The effect of weight limitations on the parameters of the optimum motion of a variable-mass body in a gravitational field is considered. An analysis is made of the optimum motion for three possible propulsion systems: limited exit velocity, limited power, and limited thrust. Solutions are presented for some typical cases. The problems of selecting the optimum weight parameters, finding the optimum propulsion system controls, and determining the optimum trajectory are solved simultaneously.

Keywords

Variational Problem Gravitational Field Typical Case Optimum Trajectory Propulsion System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Grodzovsky, G. L., Ivanov, Yu. N., andTokarev, V. V.,Low-Thrust Space Flight Mechanics (in Russian), Nauka Press, Moscow, USSR, 1966.Google Scholar
  2. 2.
    Irving, J. H., andBlum, E. K.,Comparative Performance of Ballistic and Low-Thrust Vehicles for Flight to Mars, Vistas in Astronautics, Vol. 2, Edited by M. Alperin, Pergamon Press, New York, 1959.Google Scholar
  3. 3.
    Grodzovsky, G. L., Ivanov, Yu. N., andTokarev, V. V.,On the Motion of a Body of Variable Mass with Constant Expenditure of Power in a Gravitational Field, Soviet Physics-Doklady, Vol. 6, No. 4, 1961.Google Scholar
  4. 4.
    Isaev, V. K., Sonin, V. V., andDavidson, B. Kh.,Optimal Modes of Motion of a Point with Variable Mass and Limited Power in a Homogeneous Central Field, Cosmic Research, Vol. 2, No. 4, 1964.Google Scholar
  5. 5.
    Isaev, V. K.,L. S. Pontriagin Maximum Principle and Optimal Programming of Rocket Thrust, Automation and Remote Control, Vol. 22, No. 8, 1961.Google Scholar
  6. 6.
    Grodzovsky, G. L.,Some Variational Problems of Space Flight Mechanics, Soviet Engineering Journal, Vol. 6, No. 5, 1966.Google Scholar
  7. 7.
    Miele, A.,Flight Mechanics (in Russian), Nauka Press, Moscow, USSR, 1965.Google Scholar
  8. 8.
    Barrere, E. M., Jaumotte, A., De Veubeke, B. F., andVandenkerchove, J.,Rocket Engines (in Russian), Oborongiz, Moscow, USSR, 1962.Google Scholar
  9. 9.
    Okhotsimskii, D. E.,On the Theory of Rocket Motion, PMM, Vol. 10, No. 2, 1946.Google Scholar
  10. 10.
    Okhotsimskii, D. E., andEneev, T. M.,Some Variational Problems Associated with Artificial Earth Satellite Launching (in Russian), Uspekhi Fizicheskikh Nauk, Vol. 63, No. 1a, 1957.Google Scholar
  11. 11.
    Miele, A., andCappellari, G. O.,Topics in Dynamic Programming for Rockets, ZFW, Vol. 7, No. 1, 1959.Google Scholar
  12. 12.
    Breakwell, J. V.,Optimization of Trajectories, SIAM Journal on Applied Mathematics, Vol. 7, No. 2, 1959.Google Scholar
  13. 13.
    Leitmann, G.,On a Class of Variation Problems in Rocket Flight, Journal of the Aerospace Sciences, Vol. 26, No. 9, 1959.Google Scholar
  14. 14.
    Lawden, D. F.,Optimal Intermediate-Thrust Arcs in a Gravitation Field, Astronautica Acta, Vol. 8, No. 8, 1962.Google Scholar
  15. 15.
    Contensou, P.,Theoretical Study of Optimal Trajectories in a Gravitational Field, Astronautica Acta, Vol. 8, No. 8, 1962.Google Scholar
  16. 16.
    Lawden, D. F.,Optimal Trajectories for Space Navigation, Butterworths, London, 1963.Google Scholar
  17. 17.
    Kuzmak, G. E., Isaev, V. K., andDavidson, B. Kh.,Optimality Conditions for the Motion of a Point of Variable Mass in a Homogeneous Central Field, Soviet Physics-Doklady, Vol. 8, No. 3, 1963.Google Scholar
  18. 18.
    Pontriagin, L. S., Boltiansky, V. G., Mishchenko, E. F., andGamkrelidze, R. V.,Mathematical Theory of Optimal Processes (in Russian), Fizmatgiz, Moscow, USSR, 1961.Google Scholar
  19. 19.
    Cross, C. A.,An Analogue Computer for the Vertical Rocket Landing and Take-off Problem, Journal of the British Interplanetary Society, Vol. 15, No. 1, 1956.Google Scholar
  20. 20.
    Wrobel, J. R., andBreshcars, R. R.,Lunar Landing Vehicle Propulsion Requirements, ARS Journal, Vol. 31, No. 11, 1961.Google Scholar
  21. 21.
    Malina, F. G., andSmith, A. M.,Flight Analysis of the Sounding Rocket, Journal of the Aeronautical Sciences, Vol. 5, No. 5, 1938.Google Scholar
  22. 22.
    Berman, L. J.,Optimum Soft-Landing Trajectories, Proceedings of the 12th International Astronautical Congress, Vienna, Austria, 1963.Google Scholar
  23. 23.
    Moeckel, W.,Trajectories with Constant Tangential Thrust in Central Gravitational Fields, NASA TR No. R-53, 1959.Google Scholar
  24. 24.
    Demetriades, S. T.,A Novel System for Space Flight Using a Propulsive Fluid Accumulator, Journal of the British Interplanetary Society, Vol. 17, No. 5, 1959.Google Scholar
  25. 25.
    Camac, M., andBerner, F.,An Orbital Air-Scooping Vehicle, Astronautics, Vol. 6, No. 8, 1961.Google Scholar
  26. 26.
    Reichel, R. H.,Smith, T. L., andHanford, D. R.,Potentialities of Air-Scooping Electrical Space Propulsion System, Electrical Propulsion Development, Progress in Astronautics and Aeronautics, Vol. 9, No. 9, 1963.Google Scholar
  27. 27.
    Tokarev, V. V., andFatkin, Iu. M.,Accumulator of Propulsive Substance in Problems of Optimizing Power-Limited Motion, Soviet Engineering Journal, Vol. 5, No. 3, 1965.Google Scholar

Copyright information

© Plenum Publishing Corporation 1969

Authors and Affiliations

  • G. L. Grodzovsky
    • 1
    • 2
  1. 1.Moscow Physical-Technical InstituteMoscowUSSR
  2. 2.Referativnyi Zhurnal, MekhanikaAcademy of Sciences of the USSRMoscowUSSR

Personalised recommendations