Abstract
In the algebraA of functions periodic in the mean anomaly we relate the problem of integrating over the mean anomaly with that of decomposing an element ofA as the direct sum of two functions, one in the kernel of the Lie derivative in the Keplerian flow and one in the image of this Lie derivative. We propose recursive rules amenable to general purpose symbolic processors for accomplishing such decomposition in a wide subclass ofA. We introduce the dilogarithmic function to express in exact terms quadratures involving the equation of the center.
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Osácar, C., Palacián, J. Decomposition of functions for elliptic orbits. Celestial Mech Dyn Astr 60, 207–223 (1994). https://doi.org/10.1007/BF00693322
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DOI: https://doi.org/10.1007/BF00693322