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Computing derivatives of a gravity potential by using automatic differentiation

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Abstract

A new method, based on automatic differentiation technique, has been proposed in this paper to compute the derivatives of the gravity potential. Using this method we can obtain derivatives up to any order. Instead of explicit expressions of the derivatives we use an iterative scheme to simultaneously compute the value of all the desired derivatives. The algorithm here presented can be easily parallelized by using OpenMP with the consequent improvement in CPU-time efficiency.

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Acknowledgments

This research has been supported by the Spanish Ministry of Science and Technology project MTM2012-31883, and the Bolivarian Republic of Venezuela MPPCTI/FIDETEL project FID-003-2012.

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  1. Grupo de Mecánica Espacial, IUMA, University of Zaragoza, Zaragoza, Spain

    Alberto Abad & Elvis Lacruz

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  1. Alberto Abad
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  2. Elvis Lacruz
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Correspondence to Alberto Abad.

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Abad, A., Lacruz, E. Computing derivatives of a gravity potential by using automatic differentiation. Celest Mech Dyn Astr 117, 187–200 (2013). https://doi.org/10.1007/s10569-013-9505-8

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  • DOI: https://doi.org/10.1007/s10569-013-9505-8

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