Ir al contenido (pulsa Retorno)

Universitat Politècnica de Catalunya

    • Català
    • Castellano
    • English
    • LoginRegisterLog in (no UPC users)
  • mailContact Us
  • world English 
    • Català
    • Castellano
    • English
  • userLogin   
      LoginRegisterLog in (no UPC users)

UPCommons. Global access to UPC knowledge

Banner header
69.086 UPC E-Prints
You are here:
View Item 
  •   DSpace Home
  • E-prints
  • Departaments
  • Departament de Matemàtiques
  • Articles de revista
  • View Item
  •   DSpace Home
  • E-prints
  • Departaments
  • Departament de Matemàtiques
  • Articles de revista
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Arnold's mechanism of diffusion in the spatial circular restricted three-body problem: A semi-analytical argument

Thumbnail
View/Open
SCRTBP_final.pdf (275,8Kb)
 
10.1016/j.physd.2016.06.005
 
  View UPCommons Usage Statistics
  LA Referencia / Recolecta stats
Includes usage data since 2022
Cita com:
hdl:2117/101125

Show full item record
Delshams Valdés, AmadeuMés informacióMés informacióMés informació
Gidea, Marian
Roldán, Pablo
Document typeArticle
Defense date2016-11-01
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
This work is protected by the corresponding intellectual and industrial property rights. Except where otherwise noted, its contents are licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
We consider the spatial circular restricted three-body problem, on the motion of an infinitesimal body under the gravity of Sun and Earth. This can be described by a 3-degree of freedom Hamiltonian system. We fix an energy level close to that of the collinear libration point L1, located between Sun and Earth. Near L1 there exists a normally hyperbolic invariant manifold, diffeomorphic to a 3-sphere. For an orbit confined to this 3-sphere, the amplitude of the motion relative to the ecliptic (the plane of the orbits of Sun and Earth) can vary only slightly. We show that we can obtain new orbits whose amplitude of motion relative to the ecliptic changes significantly, by following orbits of the flow restricted to the 3-sphere alternatively with homoclinic orbits that turn around the Earth. We provide an abstract theorem for the existence of such ‘diffusing’ orbits, and numerical evidence that the premises of the theorem are satisfied in the three-body problem considered here. We provide an explicit construction of diffusing orbits. The geometric mechanism underlying this construction is reminiscent of the Arnold diffusion problem for Hamiltonian systems. Our argument, however, does not involve transition chains of tori as in the classical example of Arnold. We exploit mostly the ‘outer dynamics’ along homoclinic orbits, and use very little information on the ‘inner dynamics’ restricted to the 3-sphere. As a possible application to astrodynamics, diffusing orbits as above can be used to design low cost maneuvers to change the inclination of an orbit of a satellite near L1 from a nearly-planar orbit to a tilted orbit with respect to the ecliptic. We explore different energy levels, and estimate the largest orbital inclination that can be achieved through our construction.
CitationDelshams, A., Gidea, Marian, Roldán, P. Arnold's mechanism of diffusion in the spatial circular restricted three-body problem: A semi-analytical argument. "Physica. D, Nonlinear phenomena", 1 Novembre 2016, vol. 334, p. 29-48. 
URIhttp://hdl.handle.net/2117/101125
DOI10.1016/j.physd.2016.06.005
ISSN0167-2789
Publisher versionhttp://www.sciencedirect.com/science/article/pii/S0167278916303001
Collections
  • Departament de Matemàtiques - Articles de revista [3.473]
  • SD - Sistemes Dinàmics de la UPC - Articles de revista [137]
  View UPCommons Usage Statistics

Show full item record

FilesDescriptionSizeFormatView
SCRTBP_final.pdf275,8KbPDFView/Open

Browse

This CollectionBy Issue DateAuthorsOther contributionsTitlesSubjectsThis repositoryCommunities & CollectionsBy Issue DateAuthorsOther contributionsTitlesSubjects

© UPC Obrir en finestra nova . Servei de Biblioteques, Publicacions i Arxius

info.biblioteques@upc.edu

  • About This Repository
  • Metadata under:Metadata under CC0
  • Contact Us
  • Send Feedback
  • Privacy Settings
  • Inici de la pàgina