Rigorous treatment of the averaging process for co-orbital motions in the planetary problem View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2016-10

AUTHORS

Philippe Robutel, Laurent Niederman, Alexandre Pousse

ABSTRACT

We develop a rigorous analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. By constructing a complex domain of holomorphy for the planetary Hamiltonian, we estimate the size of the transformation that maps this Hamiltonian to its first order averaged over one of the fast angles. After having derived an integrable approximation of the averaged problem, we bound the distance between this integrable approximation and the averaged Hamiltonian. This finally allows to prove rigorous theorems on the behavior of co-orbital motions over a finite but large timescale. More... »

PAGES

675-699

References to SciGraph publications

  • 1995-07. Stability of the planetary three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2011-10. The planetary N-body problem: symplectic foliation, reductions and invariant tori in INVENTIONES MATHEMATICAE
  • 1993-05. Nekhoroshev estimates for quasi-convex hamiltonian systems in MATHEMATISCHE ZEITSCHRIFT
  • 2002-04. A Perturbative Treatment of The Co-Orbital Motion in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1977-04. An asymptotic solution for the Trojan case of the plane elliptic restricted problem of three bodies in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2013-09. On the co-orbital motion of two planets in quasi-circular orbits in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2009-06. The 1/1 resonance in extrasolar planetary systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1992. Introduction to Hamiltonian Dynamical Systems and the N-Body Problem in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s40314-015-0288-2

    DOI

    http://dx.doi.org/10.1007/s40314-015-0288-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1006053341


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Numerical and Computational Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Institut de Mecanique Celeste et de Calcul des Ephemerides", 
              "id": "https://www.grid.ac/institutes/grid.462516.2", 
              "name": [
                "IMCCE, Observatoire de Paris, UPMC, CNRS UMR 8028, 77 Av. Denfert-Rochereau, 75014, Paris, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Robutel", 
            "givenName": "Philippe", 
            "id": "sg:person.015026413031.40", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015026413031.40"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "D\u00e9partement de Math\u00e9matiques", 
              "id": "https://www.grid.ac/institutes/grid.463900.8", 
              "name": [
                "IMCCE, Observatoire de Paris, UPMC, CNRS UMR 8028, 77 Av. Denfert-Rochereau, 75014, Paris, France", 
                "LMO, \u00c9quipe Topologie et Dynamique, Universit\u00e9 Paris XI, B\u00e2timent 425, 91405, Orsay, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Niederman", 
            "givenName": "Laurent", 
            "id": "sg:person.012643157161.88", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012643157161.88"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Institut de Mecanique Celeste et de Calcul des Ephemerides", 
              "id": "https://www.grid.ac/institutes/grid.462516.2", 
              "name": [
                "IMCCE, Observatoire de Paris, UPMC, CNRS UMR 8028, 77 Av. Denfert-Rochereau, 75014, Paris, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Pousse", 
            "givenName": "Alexandre", 
            "id": "sg:person.012020512141.70", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012020512141.70"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf03025718", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001281283", 
              "https://doi.org/10.1007/bf03025718"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf03025718", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001281283", 
              "https://doi.org/10.1007/bf03025718"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00692088", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016401816", 
              "https://doi.org/10.1007/bf00692088"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.1482148", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018789463"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1015219113959", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027012632", 
              "https://doi.org/10.1023/a:1015219113959"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1006/icar.1998.6032", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027567596"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10569-013-9487-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035509990", 
              "https://doi.org/10.1007/s10569-013-9487-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00222-011-0313-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039228501", 
              "https://doi.org/10.1007/s00222-011-0313-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1111/j.1365-2966.2010.16904.x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041347230"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1111/j.1365-2966.2010.16904.x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041347230"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10569-009-9185-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045676684", 
              "https://doi.org/10.1007/s10569-009-9185-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10569-009-9185-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045676684", 
              "https://doi.org/10.1007/s10569-009-9185-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1050664701", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4757-4073-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050664701", 
              "https://doi.org/10.1007/978-1-4757-4073-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4757-4073-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050664701", 
              "https://doi.org/10.1007/978-1-4757-4073-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01228428", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051519552", 
              "https://doi.org/10.1007/bf01228428"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01228428", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051519552", 
              "https://doi.org/10.1007/bf01228428"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s0143385703000397", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053858667"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/0004-6361:20010141", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1056926625"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1070/rm1963v018n06abeh001143", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058193727"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2016-10", 
        "datePublishedReg": "2016-10-01", 
        "description": "We develop a rigorous analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. By constructing a complex domain of holomorphy for the planetary Hamiltonian, we estimate the size of the transformation that maps this Hamiltonian to its first order averaged over one of the fast angles. After having derived an integrable approximation of the averaged problem, we bound the distance between this integrable approximation and the averaged Hamiltonian. This finally allows to prove rigorous theorems on the behavior of co-orbital motions over a finite but large timescale.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s40314-015-0288-2", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1284620", 
            "issn": [
              "2238-3603", 
              "0101-8205"
            ], 
            "name": "Computational and Applied Mathematics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "35"
          }
        ], 
        "name": "Rigorous treatment of the averaging process for co-orbital motions in the planetary problem", 
        "pagination": "675-699", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "1cd5e748887aecb8679cd014b06c4cebb657c37d65f1afbada7d4bc3db032def"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s40314-015-0288-2"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1006053341"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s40314-015-0288-2", 
          "https://app.dimensions.ai/details/publication/pub.1006053341"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T02:07", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8700_00000520.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2Fs40314-015-0288-2"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s40314-015-0288-2'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s40314-015-0288-2'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s40314-015-0288-2'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s40314-015-0288-2'


     

    This table displays all metadata directly associated to this object as RDF triples.

    131 TRIPLES      21 PREDICATES      42 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s40314-015-0288-2 schema:about anzsrc-for:01
    2 anzsrc-for:0103
    3 schema:author N4f4972405a19480985188ed917ab8be7
    4 schema:citation sg:pub.10.1007/978-1-4757-4073-8
    5 sg:pub.10.1007/bf00692088
    6 sg:pub.10.1007/bf01228428
    7 sg:pub.10.1007/bf03025718
    8 sg:pub.10.1007/s00222-011-0313-z
    9 sg:pub.10.1007/s10569-009-9185-6
    10 sg:pub.10.1007/s10569-013-9487-6
    11 sg:pub.10.1023/a:1015219113959
    12 https://app.dimensions.ai/details/publication/pub.1050664701
    13 https://doi.org/10.1006/icar.1998.6032
    14 https://doi.org/10.1017/s0143385703000397
    15 https://doi.org/10.1051/0004-6361:20010141
    16 https://doi.org/10.1063/1.1482148
    17 https://doi.org/10.1070/rm1963v018n06abeh001143
    18 https://doi.org/10.1111/j.1365-2966.2010.16904.x
    19 schema:datePublished 2016-10
    20 schema:datePublishedReg 2016-10-01
    21 schema:description We develop a rigorous analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. By constructing a complex domain of holomorphy for the planetary Hamiltonian, we estimate the size of the transformation that maps this Hamiltonian to its first order averaged over one of the fast angles. After having derived an integrable approximation of the averaged problem, we bound the distance between this integrable approximation and the averaged Hamiltonian. This finally allows to prove rigorous theorems on the behavior of co-orbital motions over a finite but large timescale.
    22 schema:genre research_article
    23 schema:inLanguage en
    24 schema:isAccessibleForFree true
    25 schema:isPartOf N24be25c4e4b34b829c008ffeb6732c5e
    26 Nfdde76f4ca0d4c829de7cea457bf9849
    27 sg:journal.1284620
    28 schema:name Rigorous treatment of the averaging process for co-orbital motions in the planetary problem
    29 schema:pagination 675-699
    30 schema:productId N5bca3e884eeb432b84ced916e357b5e5
    31 N8d5854e5953b46079da1219860fe6685
    32 Na3f6a0ec26d64e31a91488f61c2b5a1a
    33 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006053341
    34 https://doi.org/10.1007/s40314-015-0288-2
    35 schema:sdDatePublished 2019-04-11T02:07
    36 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    37 schema:sdPublisher Ndf0f5784814541568c49ceaac5431377
    38 schema:url http://link.springer.com/10.1007%2Fs40314-015-0288-2
    39 sgo:license sg:explorer/license/
    40 sgo:sdDataset articles
    41 rdf:type schema:ScholarlyArticle
    42 N08e86a8c946a43a7b34ed3926eac13c6 rdf:first sg:person.012020512141.70
    43 rdf:rest rdf:nil
    44 N1341168f0210440c8d96fad438e9b9d0 rdf:first sg:person.012643157161.88
    45 rdf:rest N08e86a8c946a43a7b34ed3926eac13c6
    46 N24be25c4e4b34b829c008ffeb6732c5e schema:issueNumber 3
    47 rdf:type schema:PublicationIssue
    48 N4f4972405a19480985188ed917ab8be7 rdf:first sg:person.015026413031.40
    49 rdf:rest N1341168f0210440c8d96fad438e9b9d0
    50 N5bca3e884eeb432b84ced916e357b5e5 schema:name doi
    51 schema:value 10.1007/s40314-015-0288-2
    52 rdf:type schema:PropertyValue
    53 N8d5854e5953b46079da1219860fe6685 schema:name dimensions_id
    54 schema:value pub.1006053341
    55 rdf:type schema:PropertyValue
    56 Na3f6a0ec26d64e31a91488f61c2b5a1a schema:name readcube_id
    57 schema:value 1cd5e748887aecb8679cd014b06c4cebb657c37d65f1afbada7d4bc3db032def
    58 rdf:type schema:PropertyValue
    59 Ndf0f5784814541568c49ceaac5431377 schema:name Springer Nature - SN SciGraph project
    60 rdf:type schema:Organization
    61 Nfdde76f4ca0d4c829de7cea457bf9849 schema:volumeNumber 35
    62 rdf:type schema:PublicationVolume
    63 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    64 schema:name Mathematical Sciences
    65 rdf:type schema:DefinedTerm
    66 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
    67 schema:name Numerical and Computational Mathematics
    68 rdf:type schema:DefinedTerm
    69 sg:journal.1284620 schema:issn 0101-8205
    70 2238-3603
    71 schema:name Computational and Applied Mathematics
    72 rdf:type schema:Periodical
    73 sg:person.012020512141.70 schema:affiliation https://www.grid.ac/institutes/grid.462516.2
    74 schema:familyName Pousse
    75 schema:givenName Alexandre
    76 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012020512141.70
    77 rdf:type schema:Person
    78 sg:person.012643157161.88 schema:affiliation https://www.grid.ac/institutes/grid.463900.8
    79 schema:familyName Niederman
    80 schema:givenName Laurent
    81 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012643157161.88
    82 rdf:type schema:Person
    83 sg:person.015026413031.40 schema:affiliation https://www.grid.ac/institutes/grid.462516.2
    84 schema:familyName Robutel
    85 schema:givenName Philippe
    86 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015026413031.40
    87 rdf:type schema:Person
    88 sg:pub.10.1007/978-1-4757-4073-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050664701
    89 https://doi.org/10.1007/978-1-4757-4073-8
    90 rdf:type schema:CreativeWork
    91 sg:pub.10.1007/bf00692088 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016401816
    92 https://doi.org/10.1007/bf00692088
    93 rdf:type schema:CreativeWork
    94 sg:pub.10.1007/bf01228428 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051519552
    95 https://doi.org/10.1007/bf01228428
    96 rdf:type schema:CreativeWork
    97 sg:pub.10.1007/bf03025718 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001281283
    98 https://doi.org/10.1007/bf03025718
    99 rdf:type schema:CreativeWork
    100 sg:pub.10.1007/s00222-011-0313-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1039228501
    101 https://doi.org/10.1007/s00222-011-0313-z
    102 rdf:type schema:CreativeWork
    103 sg:pub.10.1007/s10569-009-9185-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045676684
    104 https://doi.org/10.1007/s10569-009-9185-6
    105 rdf:type schema:CreativeWork
    106 sg:pub.10.1007/s10569-013-9487-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035509990
    107 https://doi.org/10.1007/s10569-013-9487-6
    108 rdf:type schema:CreativeWork
    109 sg:pub.10.1023/a:1015219113959 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027012632
    110 https://doi.org/10.1023/a:1015219113959
    111 rdf:type schema:CreativeWork
    112 https://app.dimensions.ai/details/publication/pub.1050664701 schema:CreativeWork
    113 https://doi.org/10.1006/icar.1998.6032 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027567596
    114 rdf:type schema:CreativeWork
    115 https://doi.org/10.1017/s0143385703000397 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053858667
    116 rdf:type schema:CreativeWork
    117 https://doi.org/10.1051/0004-6361:20010141 schema:sameAs https://app.dimensions.ai/details/publication/pub.1056926625
    118 rdf:type schema:CreativeWork
    119 https://doi.org/10.1063/1.1482148 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018789463
    120 rdf:type schema:CreativeWork
    121 https://doi.org/10.1070/rm1963v018n06abeh001143 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058193727
    122 rdf:type schema:CreativeWork
    123 https://doi.org/10.1111/j.1365-2966.2010.16904.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1041347230
    124 rdf:type schema:CreativeWork
    125 https://www.grid.ac/institutes/grid.462516.2 schema:alternateName Institut de Mecanique Celeste et de Calcul des Ephemerides
    126 schema:name IMCCE, Observatoire de Paris, UPMC, CNRS UMR 8028, 77 Av. Denfert-Rochereau, 75014, Paris, France
    127 rdf:type schema:Organization
    128 https://www.grid.ac/institutes/grid.463900.8 schema:alternateName Département de Mathématiques
    129 schema:name IMCCE, Observatoire de Paris, UPMC, CNRS UMR 8028, 77 Av. Denfert-Rochereau, 75014, Paris, France
    130 LMO, Équipe Topologie et Dynamique, Université Paris XI, Bâtiment 425, 91405, Orsay, France
    131 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...