The Lambert W function and solutions to Kepler’s equation |
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Authors: | Prasenjit Sengupta |
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Affiliation: | (1) Department of Aerospace Engineering, TAMU 3141, Texas A&M University, College Station, TX 77843-3141, USA |
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Abstract: | This paper presents a method for the truncation of infinite Fourier–Bessel representations for functions requiring a solution to Kepler’s equation. Use is made of the Lambert W function to solve for the desired index that bounds the remainder terms of the series, within the prescribed tolerance. The enforcement of a maximum on the number of Bessel functions is also useful in truncating the Bessel functions themselves, resulting in an analytical representation of the solution to a desired tolerance, without the use of infinite series. |
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Keywords: | Kepler’ s equation Lambert W function Series solution |
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