Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009aj....138..210f&link_type=abstract
The Astronomical Journal, Volume 138, Issue 1, pp. 210-218 (2009).
Astronomy and Astrophysics
Astronomy
2
Celestial Mechanics, Methods: Numerical
Scientific paper
We present an efficient solution of the initial-value problem of the torque-free rotation of a triaxial rigid body in a complete manner. The solution transforms, by means of a transition matrix, the coordinate triad attached to the rotating body as well as the body-fixed components of the rotational angular momentum vector from their initial values to the values at an arbitrary time. The transition matrix is expressed as one rotation matrix sandwiched by two wobble matrices. Their computation is significantly accelerated by (1) the rewriting of wobble matrices in terms of the body-fixed components of rotational angular momentum, (2) the evaluation of elliptic functions by addition theorems, and (3) the utilization of Maclaurin series expansion in computing various kinds of transcendental functions including the incomplete elliptic integral of the third kind for small arguments. The resulting formulation is a counterpart, in rotational dynamics, of the method of the so-called f- and g-functions to solve the initial-value problem of a Keplerian orbit efficiently.
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