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Decomposition of functions for elliptic orbits. (English) Zbl 0822.70008

Summary: In the algebra \(\mathcal A\) of functions periodic in the mean anomaly we relate the problem of integrating over the mean anomaly with that of decomposing an element of \(\mathcal A\) as the direct sum of two functions, one in the kernel of the Lie derivative in the Keplerian flow and the other 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 of \(\mathcal A\). We introduce the dilogarithmic function to express in exact terms quadratures involving the equation of the center.

MSC:

70F05 Two-body problems
70-08 Computational methods for problems pertaining to mechanics of particles and systems
68W30 Symbolic computation and algebraic computation

Software:

Mathematica
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References:

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