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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.04298 |
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| _version_ | 1866917744201433088 |
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| author | Rosaev, Alexey Plavalova, Eva |
| author_facet | Rosaev, Alexey Plavalova, Eva |
| contents | Linear equations with periodic coefficients describe the behavior of various dynamical systems. This studying is devoted to their applications to the planetary restricted three-body problem (RTBP). Here we consider the Laplace method for determining perturbation in coordinates. We show that classical theory of perturbation leads to a linear equation with periodic coefficients. Than we present a modification of Laplace method. This modification allows us to study motion over a longer time interval. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04298 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mathieu equation as a result of Laplace perturbation theory in the restricted three body problem Rosaev, Alexey Plavalova, Eva Earth and Planetary Astrophysics Linear equations with periodic coefficients describe the behavior of various dynamical systems. This studying is devoted to their applications to the planetary restricted three-body problem (RTBP). Here we consider the Laplace method for determining perturbation in coordinates. We show that classical theory of perturbation leads to a linear equation with periodic coefficients. Than we present a modification of Laplace method. This modification allows us to study motion over a longer time interval. |
| title | Mathieu equation as a result of Laplace perturbation theory in the restricted three body problem |
| topic | Earth and Planetary Astrophysics |
| url | https://arxiv.org/abs/2408.04298 |