Abstract
Chapter 11 described deterministic procedures for computing the orientation of a single spacecraft axis and estimating the accuracy of this computation. The methods described there may be used either to determine single-axis attitude or the orientation of any single axis on a three-axis stabilized spacecraft. However, when the three-axis attitude of a spacecraft is being computed, some additional formalism is appropriate. The attitude of a single axis can be parameterized either as a three-component unit vector or as a point on the unit celestial sphere, but three-axis attitude is most conveniently thought of as a coordinate transformation which transforms a set of reference axes in inertial space to a set in the spacecraft. The alternative parameterizations for this transformation are described in Section 12.1. Section 12.2 then describes three-axis attitude determination methods, and Section 12.3 introduces the covariance analysis needed to estimate the uncertainty in three-axis attitude.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abramowitz, M., and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series, No. 55, June 1964.
Bevington, Philip R., Data Reduction and Error Analysis for the Physical Sciences. New York: McGraw-Hill Book Company, 1969.
Bryson, Arthur E., Jr., and Yu-Chi Ho, Applied Optimal Control. Waltham, MA: Ginn and Company, 1969.
Cayley, A., “On the Motion of Rotation of a Solid Body,” Cambridge Mathematical Journal, Vol. III, No. 1843, p. 224–232. Reprinted in The Collected Papers of Arthur Cayley, Vol. I, Cambridge, Cambridge University Press, 1899, p. 28–35.
Davenport, P., Private Communication, 1968.
Gibbs, J. Willard, and E. B. Wilson, Vector Analysis, ed. by E. B. Wilson. New York: Scribner, 1901.
Goldstein, Herbert, Classical Mechanics. Reading, MA: Addison-Wesley Publishing Company, Inc., 1950.
Hildebrand, Francis B., Advanced Calculus for Applications. Englewood Cliffs, NJ: Prentice-Hall, Inc. 1964.
IMSL, Library 1 Reference Manual, International Mathematical and Statistical Libraries, Inc. (IMSL), Nov. 1975.
Keat, J., Analysis of Least-Squares Attitude Determination Routine DOAOP, Comp. Sc. Corp., CSC/TM-77/6034, Feb. 1977.
Klumpp, A. R., “Singularity-free Extraction of a Quaternion from a Direction Cosine Matrix,” J. Spacecraft, Vol. 13, p. 754–755, 1976.
Korn, Granino A., and Theresa M. Korn, Mathematical’Handbook for Scientists and Engineers. New York: McGraw-Hill, Inc., 1968.
Sabroff, A., R. Farrenkopf, A. Frew, and M. Gran, Investigation of the Acquisition Problem in Satellite Attitude Control, TRW Report AFFDL-TR-65–115, Dec.1965.
Shear, M. A., Optical Aspect Attitude Determination System (OASYS), Version 4.0, System Description and Operating Guide, Comp. Sc. Corp. 3000–06000–03TM, Dec. 1973.
Shear, M. A., and P.M. Smith, Infrared (IR) Attitude Determination System Communications Technology Satellite Version (CTSADS) Analytical Techniques, Comp. Sc. Corp., CSC/TM-76/6149, June 1976.
Shuster, M. D., Algorithms for Determining Optimal Attitude Solutions, Comp. Sc. Corp., CSC/TM-78/6056, April 1978a.
Shuster, M. D., Approximate Algorithms for Fast Optimal Attitude Computation, paper no. 78–1249, AIAA Guidance and Control Specialist Conference, Palo Alto, CA, Aug. 1978b.
Wahba, Grace, “A Least Squares Estimate of Satellite Attitude, Problem 65.1,” SIAM Review, p. 384–386, July 1966.
Whittaker, E. T., A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 4th edition. Cambridge: Cambridge University Press, 1937.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Wertz, J.R. (1978). Three-Axis Attitude Determination Methods. In: Wertz, J.R. (eds) Spacecraft Attitude Determination and Control. Astrophysics and Space Science Library, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9907-7_12
Download citation
DOI: https://doi.org/10.1007/978-94-009-9907-7_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-1204-2
Online ISBN: 978-94-009-9907-7
eBook Packages: Springer Book Archive