Abstract

This chapter describes the mathematical formulation of attitude dynamics. Alternative descriptions are available in many standard references, such as Goldstein [1950]; Kibble [1966]; Synge and Griffith [1959]; MacMillan [1936]; and Whittaker [1937]; and in more recent books emphasizing spacecraft applications, such as Thomson [1963] and Kaplan [1976]. Section 16.1 is concerned with equations of motion of attitude dynamics, using the notation defined in Section 12.1. Section 16.2 considers the solutions of these equations for torque-free rigid body motion and the use of these solutions in the variation-of-parameters formulation of rigid body dynamics. Section 16.3 discusses dynamics approximations appropriate for determining nutation parameters from attitude sensor data. Finally, the effects of flexible components on spacecraft dynamics are discussed in Section 16.4.

Keywords

Torque Cage Radar Sine Azimuth 

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References

  1. 1..
    Beard, R. M., J. E. Kronenfeld, H. Gotts, and D. Alderman, Evaluation of the SSS-1 Star Sensor Attitude Determination, Comp. Sc. Corp., 9101–16600–01TN, Aug. 1973.Google Scholar
  2. 2.
    Blanchard, D. L., R. M. Davis, E. A. Lawlor, and L. Beltracchi, “Design, Simulation and Flight Performance of Radio Astronomy Explorer-A Satellite,” Proceedings of the Symposium on Gravity-Gradient Attitude Stabilization, Aerospace Corp., AD-696–694, Dec. 1968.Google Scholar
  3. 3.
    Byrd, P. F. and M. D. Friedman, Handbook of Elliptic Integrals. Second Edition, Berlin: Springer-Verlag, 1971.MATHGoogle Scholar
  4. 4.
    Fitzpatrick, Philip M., Principles of Celestial Mechanics. New York: Academic Press, Inc., 1970.MATHGoogle Scholar
  5. 5.
    Flatley, T., Sun Sighting From a Spinning Spacecraft, NASA X-732–72–139, GSFC, May 1972a.Google Scholar
  6. 6.
    Flatley, T., Magnetic Active Nutation Damping on Explorer 45 (SSS-A), NASA X-732–72–140, GSFC, May 1972b.Google Scholar
  7. 7.
    Frisch, H. P., Coupled Thermally Induced Transverse Plus Torsional Vibrations of a Thin-Walled Cylinder of Open Cross Section, NASA X-732–69–530, GSFQ Dec. 1969.Google Scholar
  8. 8.
    Goldman, R. L., Influence of Thermal Distortion on the Anomalous Behavior of a Gravity Gradient Satellite, AIAA Paper No. 74–992, Aug. 1974.Google Scholar
  9. 9.
    Goldstein, Herbert, Classical Mechanics. Reading, MA: Addison-Wesley Publishing Company, Inc., 1950.Google Scholar
  10. 10.
    Gotts, H. S. and M. E. Plett, Determination of Nutation Amplitude From Measured Period Variation, Comp. Sc. Corp., 9101–16600–02TM, April 1973.Google Scholar
  11. 11.
    Gray, C. M., et al., Attitude Dynamics Data Simulator (ADSIM), version 3.1, Comp. Sc. Corp., 3000–06000–02TR, Sept. 1973.Google Scholar
  12. 12.
    Heinrichs, Joseph A., and Joseph J. Fee, Integrated Dynamic Analysis Simulation of Space Stations with Controllable Solar Arrays. NASA CR-112145 Sept. 1972.Google Scholar
  13. 13.
    Jacobi, C. G. J., Journal für Math., Vol. 39, p. 293, 1849.Google Scholar
  14. 14.
    Kaplan, Marshall H., Modern Spacecraft Dynamics and Control. New York-John Wiley & Sons, Inc., 1976.Google Scholar
  15. 15.
    Kibble, T. W. B., Classical Mechanics. London: McGraw-Hill, Inc., 1966.Google Scholar
  16. 16.
    Kraige, L. G. and J. L. Junkins, “Perturbation Formulations for Satellite Attitude Dynamics,” Celestial Mechanics, Vol. 13, p. 39–64, Feb. 1976.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Lawlor, E. A., R. M. Davis, and D. L. Blanchard, Engineering Parameter Determination From the Radio Astronomy Explorer (RAE-I) Satellite Attitude Data, AIAA Paper No. 74–789, Aug. 1974.Google Scholar
  18. 18.
    Likins, P. W., Dynamics and Control of Flexible Space Vehicles, JPL, Jan. 1970.Google Scholar
  19. 19.
    MacMillan, William D., Dynamics of Rigid Bodies. New York: McGraw-Hill, Inc., 1936.MATHGoogle Scholar
  20. 20.
    Meirovitch, Leonard, ed., Dynamics and Control of Large Flexible Spacecraft, Proceedings of the AIAA Symposium, Virginia Polytechnic Institute and State University, Blackburg, Virginia, June 13 to 15, 1977, 1977.Google Scholar
  21. 21.
    Milne-Thomson, L. M., “Jacobian Elliptic Functions and Theta Functions,” and “Elliptic Integrals,” Handbook of Mathematical Functions, Milton Abramowitz and Irene A. Stegun, editors. New York: Dover, 1965.Google Scholar
  22. 22.
    Modi, V. J., Attitude Dynamics With Flexible Appendages—A Brief Review, AIAA Paper No. 74167, Feb. 1974;Google Scholar
  23. 22a.
    Modi, V. J., J. Spacecraft, Vol. 11, p. 743–751, 1974.CrossRefGoogle Scholar
  24. 23.
    Morton, Harold S., Jr., John L. Junkins, and Jeffrey N. Blanton, “Analytical Solutions for Euler Parameters,” Celestial Mechanics, Vol. 10, p. 287–301, Nov. 1974.MathSciNetMATHCrossRefGoogle Scholar
  25. 24.
    Neville, Eric Harold, Jacobian Elliptic Functions. Second Edition, Oxford: Oxford University Press, Inc., 1951.MATHGoogle Scholar
  26. 25.
    Synge, John L. and B. Griffith, Principles of Mechanics. Third Edition, New York: McGraw-Hill, Inc., 1959.Google Scholar
  27. 26.
    Synge, J. L. and A. Schild, Tensor Calculus. Toronto: University of Toronto Press, 1964.Google Scholar
  28. 27.
    Thomson, William Tyrrell, Introduction to Space Dynamics. New York: John Wiley & Sons, Inc., 1963.Google Scholar
  29. 28.
    Whittaker, E. T., A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. Fourth Edition, Cambridge: Cambridge University Press, 1937.MATHGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1978

Authors and Affiliations

  • James R. Wertz
    • 1
  1. 1.Microcosm, Inc.TorranceUSA

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