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Generalization of the Euler Angles

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Abstract

It is shown that the Euler angles can be generalized to axes other than members of an orthonormal triad. As first shown by Davenport, the three generalized Euler axes, hereafter: Davenport axes, must still satisfy the constraint that the first two and the last two axes be mutually perpendicular if these axes are to define a universal set of attitude parameters. Expressions are given which relate the generalized Euler angles, hereafter: Davenport angles, to the 3-1-3 Euler angles of an associated direction-cosine matrix. The computation of the Davenport angles from the attitude matrix and their kinematic equation are presented. The present work offers a more direct development of the Davenport angles than Davenport’s original publication and offers additional results.

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References

  1. EULER, L. “De Motu Corporum Circa Punctum Fixum Mobilium,” Commentatio 825 indicis ENESTROEMIANI, Opera posthuma, Vol. 2, 1862, pp. 43–62, also Leonhardi Euleri Opera Omnia, Series Secunda, Opera Mechanica Et Astronomica, Basel, Vol. 9, 1968, pp. 413–441.

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  6. SHUSTER, M. D. “Deterministic Three-Axis Attitude Determination,” submitted to The Journal of the Astronautical Sciences.

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Authors and Affiliations

  1. Acme Spacecraft Company, 13017 Wisteria Drive, Box 328, Germantown, 20874, Maryland, USA

    Malcolm D. Shuster (Director of Research)

  2. Navigation and Control Systems Engineering Branch, Code 591, NASA Goddard Space Flight Center, Greenbelt, 20771, MD, USA

    F. Landis Markley (Aerospace Engineer, Guidance)

Authors
  1. Malcolm D. Shuster
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  2. F. Landis Markley
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Correspondence to Malcolm D. Shuster.

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Shuster, M.D., Markley, F.L. Generalization of the Euler Angles. J of Astronaut Sci 51, 123–132 (2003). https://doi.org/10.1007/BF03546304

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  • DOI: https://doi.org/10.1007/BF03546304

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