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A numerical scheme to integrate the rotational motion of a rigid body

Published online by Cambridge University Press:  25 May 2016

Toshio Fukushima
Toshio Fukushima*
Affiliation:
National Astronomical Observatory 2-21-1, Ohsawa, Mitaka, Tokyo 181, Japan (Internet) [email protected]

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Once, we numerically integrated the precession and nutation of a spheroidal rigid Earth (Kubo and Fukushima 1987). As a natural extension, we tried to integrate the rotation of a triaxial rigid Earth numerically and faced a problem: a loss of precision in long-term integration. This is due to the smallness of the characteristic period of the problem: 1 day. Of course, one can integrate the rotational motion in higher precision arithmetics with a smaller stepsize. However, the quadruple precision integration is roughly 30 times more time-consuming than the double precision integration. See Table 1. Therefore, it is desirable if there is a formulation 1) reducing the overall integration error, 2) being independent on the choice of the integrator and 3) requiring no extra computations. The key points to achieve this goal will be to find a set of variables which 1) are efficiently convertible to the physical quantities required finally, say, the orientation matrix in the case of the rotational dynamics, and 2) vary with time as smoothly as possible. In this note, we report a discovery of such an example.

Type
Part VI - Earth and Deformable Celestial Bodies
Information
Symposium - International Astronomical Union , Volume 172: Dynamics, Ephemerides and Astrometry of the Solar System , 1996 , pp. 245 - 248
Copyright
Copyright © Kluwer 1996 

References

Fukushima, T. (1994) New Canonical Variables for Orbital and Rotational Motions, Celestial Mechanics and Dynamical Astronomy, 60, 57–68.CrossRefGoogle Scholar
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Kubo, Y., and Fukushima, T. (1986) Numerical Integration of Precession and Nutation of the Rigid Earth, in The Earth's Rotation and Reference Frames for Geodesy and Geodynamics, ed. by Wilkins, G.A. and Babcock, A.K., Proc. of IAU Symp. No.128, Reidel, Dordrecht, 331–340.Google Scholar
Touma, J., and Wisdom, J. (1994) Lie-Poisson Integrators for Rigid Body Dynamics in the Solar System, Astron. J., 107, 1189–1202.CrossRefGoogle Scholar