On the global solution in the resonance problem of Poincaré View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1973-04

AUTHORS

Alan H. Jupp

ABSTRACT

Poincaré formulated a general problem of resonance in the case of a dynamical system which is reducible to one degree of freedom. He introduced the concept of a global solution; in essence, this means that the domain of the solution(s) covers the entire phase plane, comprising regions of libration and circulation.It is the author's opinion that the technique proposed by Poincaré for the construction of a global solution is impractical. Indeed, in §§201 and 211 ofLes méthodes nouvelles de la méchanique céleste, where he describes the passage from shallow resonance to deep resonance, Poincaré asserts an erroneous conclusion. An alternative procedure, which admits secular terms into the determining function and introduces a regularizing function, is outlined. The latter method has been successfully applied to the Ideal Resonance Problem, which is a special case of the more general problem considered by Poincaré, (Garfinkelet al. (1971); Garfinkel (1972). More... »

PAGES

347-355

References to SciGraph publications

  • 1972-03. Regularization in the Ideal Resonance Problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01227854

    DOI

    http://dx.doi.org/10.1007/bf01227854

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1035850236


    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/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Applied Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Dept. of Applied Mathematics, Liverpool University, England", 
              "id": "http://www.grid.ac/institutes/grid.10025.36", 
              "name": [
                "Dept. of Applied Mathematics, Liverpool University, England"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Jupp", 
            "givenName": "Alan H.", 
            "id": "sg:person.07420122720.37", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07420122720.37"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01229521", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000640735", 
              "https://doi.org/10.1007/bf01229521"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1973-04", 
        "datePublishedReg": "1973-04-01", 
        "description": "Poincar\u00e9 formulated a general problem of resonance in the case of a dynamical system which is reducible to one degree of freedom. He introduced the concept of a global solution; in essence, this means that the domain of the solution(s) covers the entire phase plane, comprising regions of libration and circulation.It is the author's opinion that the technique proposed by Poincar\u00e9 for the construction of a global solution is impractical. Indeed, in \u00a7\u00a7201 and 211 ofLes m\u00e9thodes nouvelles de la m\u00e9chanique c\u00e9leste, where he describes the passage from shallow resonance to deep resonance, Poincar\u00e9 asserts an erroneous conclusion. An alternative procedure, which admits secular terms into the determining function and introduces a regularizing function, is outlined. The latter method has been successfully applied to the Ideal Resonance Problem, which is a special case of the more general problem considered by Poincar\u00e9, (Garfinkelet al. (1971); Garfinkel (1972).", 
        "genre": "article", 
        "id": "sg:pub.10.1007/bf01227854", 
        "inLanguage": "en", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136436", 
            "issn": [
              "0008-8714", 
              "0923-2958"
            ], 
            "name": "Celestial Mechanics and Dynamical Astronomy", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "7"
          }
        ], 
        "keywords": [
          "cases", 
          "alternative procedure", 
          "author's opinion", 
          "conclusion", 
          "circulation", 
          "function", 
          "opinion", 
          "procedure", 
          "degrees of freedom", 
          "passage", 
          "erroneous conclusions", 
          "resonance", 
          "degree", 
          "resonance problem", 
          "region", 
          "problem", 
          "technique", 
          "method", 
          "solution", 
          "phase plane", 
          "latter method", 
          "system", 
          "global solution", 
          "domain", 
          "terms", 
          "shallow resonance", 
          "general problem", 
          "dynamical systems", 
          "plane", 
          "construction", 
          "concept", 
          "freedom", 
          "special case", 
          "nouvelles", 
          "deep resonance", 
          "secular terms", 
          "essence", 
          "libration", 
          "Poincar\u00e9", 
          "Ideal Resonance Problem", 
          "entire phase plane", 
          "regions of libration", 
          "ofLes m\u00e9thodes nouvelles", 
          "M\u00e9thodes Nouvelles", 
          "la m\u00e9chanique c\u00e9leste", 
          "m\u00e9chanique c\u00e9leste", 
          "c\u00e9leste"
        ], 
        "name": "On the global solution in the resonance problem of Poincar\u00e9", 
        "pagination": "347-355", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1035850236"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf01227854"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf01227854", 
          "https://app.dimensions.ai/details/publication/pub.1035850236"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T18:01", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_150.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/bf01227854"
      }
    ]
     

    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/bf01227854'

    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/bf01227854'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01227854'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01227854'


     

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

    109 TRIPLES      22 PREDICATES      74 URIs      65 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf01227854 schema:about anzsrc-for:01
    2 anzsrc-for:0102
    3 schema:author Nbf168ffec7d541eba7f8a792fa16a507
    4 schema:citation sg:pub.10.1007/bf01229521
    5 schema:datePublished 1973-04
    6 schema:datePublishedReg 1973-04-01
    7 schema:description Poincaré formulated a general problem of resonance in the case of a dynamical system which is reducible to one degree of freedom. He introduced the concept of a global solution; in essence, this means that the domain of the solution(s) covers the entire phase plane, comprising regions of libration and circulation.It is the author's opinion that the technique proposed by Poincaré for the construction of a global solution is impractical. Indeed, in §§201 and 211 ofLes méthodes nouvelles de la méchanique céleste, where he describes the passage from shallow resonance to deep resonance, Poincaré asserts an erroneous conclusion. An alternative procedure, which admits secular terms into the determining function and introduces a regularizing function, is outlined. The latter method has been successfully applied to the Ideal Resonance Problem, which is a special case of the more general problem considered by Poincaré, (Garfinkelet al. (1971); Garfinkel (1972).
    8 schema:genre article
    9 schema:inLanguage en
    10 schema:isAccessibleForFree false
    11 schema:isPartOf N110f108b55a1442aa87523ec57137008
    12 Nadc1299d640847e198ca266630b11e5a
    13 sg:journal.1136436
    14 schema:keywords Ideal Resonance Problem
    15 Méthodes Nouvelles
    16 Poincaré
    17 alternative procedure
    18 author's opinion
    19 cases
    20 circulation
    21 concept
    22 conclusion
    23 construction
    24 céleste
    25 deep resonance
    26 degree
    27 degrees of freedom
    28 domain
    29 dynamical systems
    30 entire phase plane
    31 erroneous conclusions
    32 essence
    33 freedom
    34 function
    35 general problem
    36 global solution
    37 la méchanique céleste
    38 latter method
    39 libration
    40 method
    41 méchanique céleste
    42 nouvelles
    43 ofLes méthodes nouvelles
    44 opinion
    45 passage
    46 phase plane
    47 plane
    48 problem
    49 procedure
    50 region
    51 regions of libration
    52 resonance
    53 resonance problem
    54 secular terms
    55 shallow resonance
    56 solution
    57 special case
    58 system
    59 technique
    60 terms
    61 schema:name On the global solution in the resonance problem of Poincaré
    62 schema:pagination 347-355
    63 schema:productId N3b083003fd3a4df5911ca3d485581135
    64 N8fa8b008812b4fd586d68f45816d1be7
    65 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035850236
    66 https://doi.org/10.1007/bf01227854
    67 schema:sdDatePublished 2022-01-01T18:01
    68 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    69 schema:sdPublisher N6508654e9729444e8977ea5345e7bed6
    70 schema:url https://doi.org/10.1007/bf01227854
    71 sgo:license sg:explorer/license/
    72 sgo:sdDataset articles
    73 rdf:type schema:ScholarlyArticle
    74 N110f108b55a1442aa87523ec57137008 schema:volumeNumber 7
    75 rdf:type schema:PublicationVolume
    76 N3b083003fd3a4df5911ca3d485581135 schema:name dimensions_id
    77 schema:value pub.1035850236
    78 rdf:type schema:PropertyValue
    79 N6508654e9729444e8977ea5345e7bed6 schema:name Springer Nature - SN SciGraph project
    80 rdf:type schema:Organization
    81 N8fa8b008812b4fd586d68f45816d1be7 schema:name doi
    82 schema:value 10.1007/bf01227854
    83 rdf:type schema:PropertyValue
    84 Nadc1299d640847e198ca266630b11e5a schema:issueNumber 3
    85 rdf:type schema:PublicationIssue
    86 Nbf168ffec7d541eba7f8a792fa16a507 rdf:first sg:person.07420122720.37
    87 rdf:rest rdf:nil
    88 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    89 schema:name Mathematical Sciences
    90 rdf:type schema:DefinedTerm
    91 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
    92 schema:name Applied Mathematics
    93 rdf:type schema:DefinedTerm
    94 sg:journal.1136436 schema:issn 0008-8714
    95 0923-2958
    96 schema:name Celestial Mechanics and Dynamical Astronomy
    97 schema:publisher Springer Nature
    98 rdf:type schema:Periodical
    99 sg:person.07420122720.37 schema:affiliation grid-institutes:grid.10025.36
    100 schema:familyName Jupp
    101 schema:givenName Alan H.
    102 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07420122720.37
    103 rdf:type schema:Person
    104 sg:pub.10.1007/bf01229521 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000640735
    105 https://doi.org/10.1007/bf01229521
    106 rdf:type schema:CreativeWork
    107 grid-institutes:grid.10025.36 schema:alternateName Dept. of Applied Mathematics, Liverpool University, England
    108 schema:name Dept. of Applied Mathematics, Liverpool University, England
    109 rdf:type schema:Organization
     




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


    ...