On the Stability of Realistic Three-Body Problems View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1997-06

AUTHORS

Alessandra Celletti, Luigi Chierchia

ABSTRACT

We consider the system Sun—Jupiter—Ceres as an example of a planar, circular, restricted three-body problem and, after substituting the mass ratio of Jupiter/Sun (which is approximately 10-3) with a parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, we prove the existence of stable quasi-periodic motions with frequencies close to the observed (average) frequencies reported in “The Astronomical Almanac” for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. The proof is “computer-assisted”. More... »

PAGES

413-449

References to SciGraph publications

  • 1995-07. Stability of the planetary three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1988-03. Construction of analytic KAM surfaces and effective stability bounds in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1995. A Constructive Theory of Lagrangian Tori and Computer-assisted Applications in DYNAMICS REPORTED
  • 1990-03. Analysis of resonances in the spin-orbit problem in Celestial Mechanics: The synchronous resonance (Part I) in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 1989-12. KAM theory in configuration space in COMMENTARII MATHEMATICI HELVETICI
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s002200050115

    DOI

    http://dx.doi.org/10.1007/s002200050115

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1021268156


    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/2008/0201", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Astronomical and Space Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/02", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Physical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "University of L'Aquila", 
              "id": "https://www.grid.ac/institutes/grid.158820.6", 
              "name": [
                "Dipartimento di Matematica,  Universit\u00e0 dell'Aquila, 67100\u2014Coppito, L'Aquila, Italy.\u00b6E-mail: celletti@axscaq.aquila.infn.it, IT"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Celletti", 
            "givenName": "Alessandra", 
            "id": "sg:person.010640371067.72", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010640371067.72"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Roma Tre University", 
              "id": "https://www.grid.ac/institutes/grid.8509.4", 
              "name": [
                "Dipartimento di Matematica,  Universit\u00e0: di Roma Tre, Largo San Murialdo 1, 00146 Roma, Italy.\u00b6E-mail: luigi@matrm3.mat.uniroma3.it, IT"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Chierchia", 
            "givenName": "Luigi", 
            "id": "sg:person.011416060407.17", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011416060407.17"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf02564665", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008438703", 
              "https://doi.org/10.1007/bf02564665"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-61215-2_2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014474523", 
              "https://doi.org/10.1007/978-3-642-61215-2_2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00692089", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016738552", 
              "https://doi.org/10.1007/bf00692089"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00945107", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038135595", 
              "https://doi.org/10.1007/bf00945107"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01218480", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051900418", 
              "https://doi.org/10.1007/bf01218480"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01218480", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051900418", 
              "https://doi.org/10.1007/bf01218480"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.3068879", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057908491"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/s0036144595284180", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062877881"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1997-06", 
        "datePublishedReg": "1997-06-01", 
        "description": "We consider the system Sun\u2014Jupiter\u2014Ceres as an example of a planar, circular, restricted three-body problem and, after substituting the mass ratio of Jupiter/Sun (which is approximately 10-3) with a parameter \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}\\end{document}, we prove the existence of stable quasi-periodic motions with frequencies close to the observed (average) frequencies reported in \u201cThe Astronomical Almanac\u201d for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}\\end{document}. The proof is \u201ccomputer-assisted\u201d.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s002200050115", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136216", 
            "issn": [
              "0010-3616", 
              "1432-0916"
            ], 
            "name": "Communications in Mathematical Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "186"
          }
        ], 
        "name": "On the Stability of Realistic Three-Body Problems", 
        "pagination": "413-449", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "65550d8f9225316ba22f4be4d6c2e5c7978870e86dae961eaf87369d414b4e22"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s002200050115"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1021268156"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s002200050115", 
          "https://app.dimensions.ai/details/publication/pub.1021268156"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T21:37", 
        "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_8687_00000512.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2Fs002200050115"
      }
    ]
     

    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/s002200050115'

    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/s002200050115'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s002200050115'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s002200050115'


     

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

    97 TRIPLES      21 PREDICATES      34 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s002200050115 schema:about anzsrc-for:02
    2 anzsrc-for:0201
    3 schema:author Nf2d3fa72246b4884bf27dc2e678aea00
    4 schema:citation sg:pub.10.1007/978-3-642-61215-2_2
    5 sg:pub.10.1007/bf00692089
    6 sg:pub.10.1007/bf00945107
    7 sg:pub.10.1007/bf01218480
    8 sg:pub.10.1007/bf02564665
    9 https://doi.org/10.1063/1.3068879
    10 https://doi.org/10.1137/s0036144595284180
    11 schema:datePublished 1997-06
    12 schema:datePublishedReg 1997-06-01
    13 schema:description We consider the system Sun—Jupiter—Ceres as an example of a planar, circular, restricted three-body problem and, after substituting the mass ratio of Jupiter/Sun (which is approximately 10-3) with a parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, we prove the existence of stable quasi-periodic motions with frequencies close to the observed (average) frequencies reported in “The Astronomical Almanac” for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. The proof is “computer-assisted”.
    14 schema:genre research_article
    15 schema:inLanguage en
    16 schema:isAccessibleForFree false
    17 schema:isPartOf N468fe38fc95449f680cf29c4d3909f0f
    18 N57d467bbee6b467b941d3fe44c6b367d
    19 sg:journal.1136216
    20 schema:name On the Stability of Realistic Three-Body Problems
    21 schema:pagination 413-449
    22 schema:productId N64f20e1d9df94acfa64178d0a69efdad
    23 N7c4cc36a141b4d34bd7d04ed5e0bfc10
    24 Necec17d0932441bfbac99f72c1938dbf
    25 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021268156
    26 https://doi.org/10.1007/s002200050115
    27 schema:sdDatePublished 2019-04-10T21:37
    28 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    29 schema:sdPublisher Nd36f81c33f78425a83c8ed509d161be7
    30 schema:url http://link.springer.com/10.1007%2Fs002200050115
    31 sgo:license sg:explorer/license/
    32 sgo:sdDataset articles
    33 rdf:type schema:ScholarlyArticle
    34 N2d4e0137431140a5b7efd070f7ae4d8f rdf:first sg:person.011416060407.17
    35 rdf:rest rdf:nil
    36 N468fe38fc95449f680cf29c4d3909f0f schema:volumeNumber 186
    37 rdf:type schema:PublicationVolume
    38 N57d467bbee6b467b941d3fe44c6b367d schema:issueNumber 2
    39 rdf:type schema:PublicationIssue
    40 N64f20e1d9df94acfa64178d0a69efdad schema:name doi
    41 schema:value 10.1007/s002200050115
    42 rdf:type schema:PropertyValue
    43 N7c4cc36a141b4d34bd7d04ed5e0bfc10 schema:name readcube_id
    44 schema:value 65550d8f9225316ba22f4be4d6c2e5c7978870e86dae961eaf87369d414b4e22
    45 rdf:type schema:PropertyValue
    46 Nd36f81c33f78425a83c8ed509d161be7 schema:name Springer Nature - SN SciGraph project
    47 rdf:type schema:Organization
    48 Necec17d0932441bfbac99f72c1938dbf schema:name dimensions_id
    49 schema:value pub.1021268156
    50 rdf:type schema:PropertyValue
    51 Nf2d3fa72246b4884bf27dc2e678aea00 rdf:first sg:person.010640371067.72
    52 rdf:rest N2d4e0137431140a5b7efd070f7ae4d8f
    53 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
    54 schema:name Physical Sciences
    55 rdf:type schema:DefinedTerm
    56 anzsrc-for:0201 schema:inDefinedTermSet anzsrc-for:
    57 schema:name Astronomical and Space Sciences
    58 rdf:type schema:DefinedTerm
    59 sg:journal.1136216 schema:issn 0010-3616
    60 1432-0916
    61 schema:name Communications in Mathematical Physics
    62 rdf:type schema:Periodical
    63 sg:person.010640371067.72 schema:affiliation https://www.grid.ac/institutes/grid.158820.6
    64 schema:familyName Celletti
    65 schema:givenName Alessandra
    66 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010640371067.72
    67 rdf:type schema:Person
    68 sg:person.011416060407.17 schema:affiliation https://www.grid.ac/institutes/grid.8509.4
    69 schema:familyName Chierchia
    70 schema:givenName Luigi
    71 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011416060407.17
    72 rdf:type schema:Person
    73 sg:pub.10.1007/978-3-642-61215-2_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014474523
    74 https://doi.org/10.1007/978-3-642-61215-2_2
    75 rdf:type schema:CreativeWork
    76 sg:pub.10.1007/bf00692089 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016738552
    77 https://doi.org/10.1007/bf00692089
    78 rdf:type schema:CreativeWork
    79 sg:pub.10.1007/bf00945107 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038135595
    80 https://doi.org/10.1007/bf00945107
    81 rdf:type schema:CreativeWork
    82 sg:pub.10.1007/bf01218480 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051900418
    83 https://doi.org/10.1007/bf01218480
    84 rdf:type schema:CreativeWork
    85 sg:pub.10.1007/bf02564665 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008438703
    86 https://doi.org/10.1007/bf02564665
    87 rdf:type schema:CreativeWork
    88 https://doi.org/10.1063/1.3068879 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057908491
    89 rdf:type schema:CreativeWork
    90 https://doi.org/10.1137/s0036144595284180 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062877881
    91 rdf:type schema:CreativeWork
    92 https://www.grid.ac/institutes/grid.158820.6 schema:alternateName University of L'Aquila
    93 schema:name Dipartimento di Matematica, Università dell'Aquila, 67100—Coppito, L'Aquila, Italy.¶E-mail: celletti@axscaq.aquila.infn.it, IT
    94 rdf:type schema:Organization
    95 https://www.grid.ac/institutes/grid.8509.4 schema:alternateName Roma Tre University
    96 schema:name Dipartimento di Matematica, Università: di Roma Tre, Largo San Murialdo 1, 00146 Roma, Italy.¶E-mail: luigi@matrm3.mat.uniroma3.it, IT
    97 rdf:type schema:Organization
     




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


    ...