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Deprit’s Elimination of the Parallax Revisited

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Abstract

An extension of Deprit’s elimination of the parallax is proposed. This extension takes advantage of the flexibility of the Lie-Deprit method, when the inverse of the Lie operator is applied in order to calculate the generating function of this Lie transform. We have found that, under certain conditions, a function \(\mathcal {F}_{n}\), belonging to the null space of the Lie operator, can be added to the generating function of the transform at each order, so that the argument of the perigee, and therefore the argument of latitude, can be fully removed in the zonal case of the artificial satellite problem.

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Acknowledgments

We would like to dedicate this work to Dr. A. Deprit (in memoriam) and all his collaborators and students, in particular to Prof. S. Ferrer, his first Spanish collaborator. We would also like to thank the anonymous reviewers for their valuable comments, which have contributed to the improvement of the article. This work has been supported in part by the Goverment of La Rioja (Project FOMENTA 10/16).

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Authors and Affiliations

  1. Department of Mathemtics and Computer Science, GRUCACI, University of La Rioja, Logroño, Spain

    Juan F. San-Juan

  2. Department of Mathemtics and Computer Science, University of La Rioja, Logroño, Spain

    David Ortigosa

  3. Department of Mechanical Engineering, University of La Rioja, Logroño, Spain

    Luis M. López-Ochoa

  4. Center for Biomedical Research of La Rioja (CIBIR), GRUCACI, University of La Rioja, Logroño, Spain

    Rosario López

Authors
  1. Juan F. San-Juan
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  2. David Ortigosa
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  3. Luis M. López-Ochoa
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  4. Rosario López
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Correspondence to Juan F. San-Juan.

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San-Juan, J.F., Ortigosa, D., López-Ochoa, L.M. et al. Deprit’s Elimination of the Parallax Revisited. J of Astronaut Sci 60, 137–148 (2013). https://doi.org/10.1007/s40295-015-0033-5

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