Symbolic iteration method based on computer algebra analysis for Kepler's equation.

ABSTRACT: The Kepler's equation of elliptic orbits is one of the most significant fundamental physical equations in Satellite Geodesy. This paper demonstrates symbolic iteration method based on computer algebra analysis (SICAA) to solve the Kepler's equation. The paper presents general symbolic formulas to compute the eccentric anomaly (E) without complex numerical iterative computation at run-time. This approach couples the Taylor series expansion with higher-order trigonometric function reductions during the symbolic iterative progress. Meanwhile, the relationship between our method and the traditional infinite series expansion solution is analyzed in this paper, obtaining a new truncation method of the series expansion solution for the Kepler's equation. We performed substantial tests on a modest

SUBMITTER: Zhang R 

PROVIDER: S-EPMC8863892 | biostudies-literature | 2022 Feb

REPOSITORIES: biostudies-literature