Abstract
The authors’ individual work on the inclination functions over a period of more than 30 years has led to the need for a joint paper. Intervening papers by other authors have demonstrated misunderstandings needing to be corrected, in particular concerning the key recurrence relation published by the present first author in 1971. This relation is remarkably stable, though this has not always been recognized. The real source of error with the specific functions that are involved in the recurrence relation arises from the possibilities for underflow (as well as overflow) in the computation. The problem exists even with normalized versions of the functions, and is carefully addressed. Very important, for both academic and practical reasons, is a general invariance relation that had been found earlier by the second author, for which a proof is given here for the first time. Some numerical results from our new (and highly efficient) procedure for computing the inclination functions are tabulated, and comparisons made with the results of other authors. Finally, Fortran code for an optimized implementation of this procedure is in supplementary material.
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Gooding, R.H., Wagner, C.A. On the inclination functions and a rapid stable procedure for their evaluation together with derivatives. Celest Mech Dyn Astr 101, 247–272 (2008). https://doi.org/10.1007/s10569-008-9145-6
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DOI: https://doi.org/10.1007/s10569-008-9145-6