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PreprintCC BY 4.0arXiv

Naturalization of Vinti's intermediary orbit---or how to get rid of small divisors in Brouwer's satellite solution

  • Martin Lara
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Abstract

A naturalization, in the sense of Deprit, of Vinti's dynamical system makes the construction of a first order analytical satellite perturbation solution without critical divisors possible. The process gives hints on how to recast Brouwer's classical solution in a form that is free from small divisors too. The functionality of classical perturbation solutions is in this way extended to the close vicinity of the critical inclination. The new analytical solution bears terms that may grow unbounded, but their negative effects do not disclose in time intervals in which this kind of solution may be useful in practice.

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Cite

BibTeXRIS
BibTeX
@misc{lara2026naturalization,
  title = {{Naturalization of Vinti's intermediary orbit---or how to get rid of small divisors in Brouwer's satellite solution}},
  author = {Martin Lara},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03701},
  eprint = {2611.03701},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03701},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Naturalization of Vinti's intermediary orbit---or how to get rid of small divisors in Brouwer's satellite solution
AU  - Martin Lara
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.03701
UR  - https://arxiv.org/abs/2611.03701
AB  - A naturalization, in the sense of Deprit, of Vinti's dynamical system makes the construction of a first order analytical satellite perturbation solution without critical divisors possible. The process gives hints on how to recast Brouwer's classical solution in a form that is free from small divisors too. The functionality of classical perturbation solutions is in this way extended to the close vicinity of the critical inclination. The new analytical solution bears terms that may grow unbounded, but their negative effects do not disclose in time intervals in which this kind of solution may be useful in practice.
ER  -