Shannon Entropy Applied to the Planar Restricted Three-Body Problem

We present a numerical study of the application of the Shannon entropy technique to the planar restricted three-body problem in the vicinity of first-order interior mean-motion resonances with the perturber. We estimate the diffusion coefficient for a series of initial conditions and compare the res...

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Autores principales: Beauge, Cristian, Cincotta, Pablo Miguel
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2019
Materias:
Astronomía
Three-Body Problem
Resonances
Stability
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/125174
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-125174
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Astronomía
Three-Body Problem
Resonances
Stability
spellingShingle Astronomía
Three-Body Problem
Resonances
Stability
Beauge, Cristian
Cincotta, Pablo Miguel
Shannon Entropy Applied to the Planar Restricted Three-Body Problem
topic_facet Astronomía
Three-Body Problem
Resonances
Stability
description We present a numerical study of the application of the Shannon entropy technique to the planar restricted three-body problem in the vicinity of first-order interior mean-motion resonances with the perturber. We estimate the diffusion coefficient for a series of initial conditions and compare the results with calculations obtained from the time evolution of the variance in the semimajor-axis and eccentricity plane. Adopting adequate normalization factors, both methods yield comparable results, although much shorter integration times are required for entropy calculations. A second advantage of the use of entropy is that it is possible to obtain reliable results even without the use of ensembles or analysis restricted to surfaces of section or representative planes. This allows for a much more numerically efficient tool that may be incorporated into a working N-body code and applied to numerous dynamical problems in planetary dynamics. Finally, we estimate instability times for a series of initial conditions in the 2/1 and 3/2 mean-motion resonances and compare them with times of escape obtained from directed N-body simulations. We find very good agreement in all cases, not only with respect to average values but also in their dispersion for near-by trajectories.
format Articulo
Preprint
author Beauge, Cristian
Cincotta, Pablo Miguel
author_facet Beauge, Cristian
Cincotta, Pablo Miguel
author_sort Beauge, Cristian
title Shannon Entropy Applied to the Planar Restricted Three-Body Problem
title_short Shannon Entropy Applied to the Planar Restricted Three-Body Problem
title_full Shannon Entropy Applied to the Planar Restricted Three-Body Problem
title_fullStr Shannon Entropy Applied to the Planar Restricted Three-Body Problem
title_full_unstemmed Shannon Entropy Applied to the Planar Restricted Three-Body Problem
title_sort shannon entropy applied to the planar restricted three-body problem
publishDate 2019
url http://sedici.unlp.edu.ar/handle/10915/125174
work_keys_str_mv AT beaugecristian shannonentropyappliedtotheplanarrestrictedthreebodyproblem
AT cincottapablomiguel shannonentropyappliedtotheplanarrestrictedthreebodyproblem
bdutipo_str Repositorios
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