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Roll Dynamics of a Spinning Axi-Symmetric Satellite using the WKBJ Method

Published online by Cambridge University Press:  04 July 2016

V. J. Modi  and
J. E. Neilson
V. J. Modi
Affiliation:
The University of British Columbia, Vancouver, BC, Canada
J. E. Neilson
Affiliation:
The University of British Columbia, Vancouver, BC, Canada
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Summary

The attitude dynamics of a spinning axi-symmetric satellite, free to librate in roll, is studied using the WKBJ method. Applicability of the method to the linearised equation of motion is first verified. To facilitate the evaluation of the WKBJ solution and to make it more amenable to the phase space analysis, second order terms in eccentricity are neglected. The form of the solution suggests the presence of phase and amplitude modulation effects for non-circular orbits. The comparison between the WKBJ analysis and ‘exact’ numerical solutions showed that the approximate analysis predicts the period and amplitude of motion with an accuracy adequate for the preliminary design purposes.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 72 , Issue 693 , September 1968 , pp. 807 - 810
Copyright
Copyright © Royal Aeronautical Society 1968 

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References

1. Cunningham, W. J., Introduction to Nonlinear Analysis, McGraw-Hill Inc., New York, pp 245, 1958.Google Scholar
2. He'non, M. and Heiles, C, The Applicability of the Third Integral of Motion: Some Numerical Experiments, Astronom J, 69, pp 73–79, 1964 Google Scholar
3. Brereton, R. C. and Modi, V. J. Stability of the Planar Librational Motion of a Satellite in an Elliptic Orbit, presented at XVII International Astronautical Congress, Madrid, Spain, 1966.Google Scholar