Abstract
The efficiency in the computation of circular functions, such as cos(u) or sin(u), where u is a Poisson series, is important to derive accurate solutions of many problems of Celestial Mechanics, for instance, the orbital or rotational perturbed motion of natural or artificial bodies, since expansions in terms of Legendre functions and multiple Fourier series appear almost everywhere. Therefore, it is worth searching for alternative algorithms with lower computational cost. In this article, we propose a method based on the idea of elimination, which was originally applied to solve numerical problems, mainly in the case of matrix functions. Our comparisons with the traditional Taylor expansion prove that this new method can be more efficient when applied to compute the sine and cosine of a Poisson series.
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Martínez, M.d.C., Navarro, J.F. & Ferrándiz, J.M. An improved algorithm to compute circular functions of Poisson series. Celestial Mech Dyn Astr 99, 59–68 (2007). https://doi.org/10.1007/s10569-007-9090-9
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DOI: https://doi.org/10.1007/s10569-007-9090-9