{"title":"Lagrange's planetary equations with time-dependent secular perturbations","authors":"Barnabás Deme","doi":"arxiv-2405.18140","DOIUrl":null,"url":null,"abstract":"The long-term evolution of astrophysical systems is driven by a Hamiltonian\nthat is independent of the fast angle. As this Hamiltonian may contain\nexplicitly time-dependent parameters, the conservation of mechanical energy is\nnot guaranteed in such systems. We derive how the semi-major axis evolves in\nthese cases. We analyze two astrophysically interesting examples, those of the\nharmonic and quadrupole perturbations.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"34 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Classical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.18140","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The long-term evolution of astrophysical systems is driven by a Hamiltonian
that is independent of the fast angle. As this Hamiltonian may contain
explicitly time-dependent parameters, the conservation of mechanical energy is
not guaranteed in such systems. We derive how the semi-major axis evolves in
these cases. We analyze two astrophysically interesting examples, those of the
harmonic and quadrupole perturbations.
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