A comparison of the Bohlin-von Zeipel and Bohlin-Lie series methods in resonant systems View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1982-04

AUTHORS

A. H. Jupp

ABSTRACT

Whereas the Bohlin-von Zeipel procedure can be used successfully to construct formal solutions to some resonant dynamical systems, it is shown here that a direct Bohlin-Lie series approach seems not to be feasible. The fact that certain terms lose an order of magnitude on differntiation with respect to the momentum variable leads to a situation which precludes an accurate construction of the first-order term in the generating function. A simple remedy to this impasse is suggested, with particular reference to theIdeal Resonance Problem. More... »

PAGES

413-422

References to SciGraph publications

  • 1969-03. Canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1973-08. The global solution of the problem of the critical inclination in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1978-10. Theory of the Trojan asteroids Part II in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1974-01. The Ideal Resonance Problem: A comparison of the solutions expressed in terms of mean elements and in terms of initial conditions in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970-03. The equivalence of von Zeipel mappings and Lie transforms in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1972-01. A second-order solution of the Ideal Resonance Problem by Lie series in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1974-03. A second-order global solution of the ideal resonance problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01230421

    DOI

    http://dx.doi.org/10.1007/bf01230421

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1002947958


    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/2008/0102", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Applied 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": "University of Liverpool", 
              "id": "https://www.grid.ac/institutes/grid.10025.36", 
              "name": [
                "Department of Applied Mathematics and Theoretical Physics, Liverpool University, England"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Jupp", 
            "givenName": "A. 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/bf01228388", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005645418", 
              "https://doi.org/10.1007/bf01228388"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01227802", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011827560", 
              "https://doi.org/10.1007/bf01227802"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01227802", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011827560", 
              "https://doi.org/10.1007/bf01227802"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01230455", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013280863", 
              "https://doi.org/10.1007/bf01230455"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01230455", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013280863", 
              "https://doi.org/10.1007/bf01230455"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01227819", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013346507", 
              "https://doi.org/10.1007/bf01227819"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01227819", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013346507", 
              "https://doi.org/10.1007/bf01227819"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01230167", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016607058", 
              "https://doi.org/10.1007/bf01230167"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01230167", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016607058", 
              "https://doi.org/10.1007/bf01230167"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01230629", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028918192", 
              "https://doi.org/10.1007/bf01230629"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01230629", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028918192", 
              "https://doi.org/10.1007/bf01230629"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01236167", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047634101", 
              "https://doi.org/10.1007/bf01236167"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01236167", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047634101", 
              "https://doi.org/10.1007/bf01236167"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1093/mnras/148.2.197", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049777061"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1086/107956", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058446683"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1086/107958", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058446685"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1086/108248", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058446954"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1086/110171", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058448772"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1086/111099", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058449678"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1982-04", 
        "datePublishedReg": "1982-04-01", 
        "description": "Whereas the Bohlin-von Zeipel procedure can be used successfully to construct formal solutions to some resonant dynamical systems, it is shown here that a direct Bohlin-Lie series approach seems not to be feasible. The fact that certain terms lose an order of magnitude on differntiation with respect to the momentum variable leads to a situation which precludes an accurate construction of the first-order term in the generating function. A simple remedy to this impasse is suggested, with particular reference to theIdeal Resonance Problem.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/bf01230421", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136436", 
            "issn": [
              "0008-8714", 
              "0923-2958"
            ], 
            "name": "Celestial Mechanics and Dynamical Astronomy", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "4", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "26"
          }
        ], 
        "name": "A comparison of the Bohlin-von Zeipel and Bohlin-Lie series methods in resonant systems", 
        "pagination": "413-422", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "0e0a3a6fbd3c58312b2e326b57a59207f1baffe16e80505c6cd481c37b6cf9e8"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf01230421"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1002947958"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf01230421", 
          "https://app.dimensions.ai/details/publication/pub.1002947958"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T13:29", 
        "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/v90/0000000370_0000000370/records_46747_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007/BF01230421"
      }
    ]
     

    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/bf01230421'

    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/bf01230421'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01230421'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01230421'


     

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

    107 TRIPLES      21 PREDICATES      40 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf01230421 schema:about anzsrc-for:01
    2 anzsrc-for:0102
    3 schema:author N7617b1af6a94480f9849aa92777e5264
    4 schema:citation sg:pub.10.1007/bf01227802
    5 sg:pub.10.1007/bf01227819
    6 sg:pub.10.1007/bf01228388
    7 sg:pub.10.1007/bf01230167
    8 sg:pub.10.1007/bf01230455
    9 sg:pub.10.1007/bf01230629
    10 sg:pub.10.1007/bf01236167
    11 https://doi.org/10.1086/107956
    12 https://doi.org/10.1086/107958
    13 https://doi.org/10.1086/108248
    14 https://doi.org/10.1086/110171
    15 https://doi.org/10.1086/111099
    16 https://doi.org/10.1093/mnras/148.2.197
    17 schema:datePublished 1982-04
    18 schema:datePublishedReg 1982-04-01
    19 schema:description Whereas the Bohlin-von Zeipel procedure can be used successfully to construct formal solutions to some resonant dynamical systems, it is shown here that a direct Bohlin-Lie series approach seems not to be feasible. The fact that certain terms lose an order of magnitude on differntiation with respect to the momentum variable leads to a situation which precludes an accurate construction of the first-order term in the generating function. A simple remedy to this impasse is suggested, with particular reference to theIdeal Resonance Problem.
    20 schema:genre research_article
    21 schema:inLanguage en
    22 schema:isAccessibleForFree false
    23 schema:isPartOf N4fb0e81864304794ab6f4e1e284c813a
    24 Ne691b77c0cc94acf8553ad02a927a542
    25 sg:journal.1136436
    26 schema:name A comparison of the Bohlin-von Zeipel and Bohlin-Lie series methods in resonant systems
    27 schema:pagination 413-422
    28 schema:productId N756b820eb484432aa25b13a683d10904
    29 Na3c8285654ad48c0ab2117140eaa1d3f
    30 Ne5948fc0be08405497e1c45166d31cf8
    31 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002947958
    32 https://doi.org/10.1007/bf01230421
    33 schema:sdDatePublished 2019-04-11T13:29
    34 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    35 schema:sdPublisher Nf791907984e64b2a8e0bd73f806959ab
    36 schema:url http://link.springer.com/10.1007/BF01230421
    37 sgo:license sg:explorer/license/
    38 sgo:sdDataset articles
    39 rdf:type schema:ScholarlyArticle
    40 N4fb0e81864304794ab6f4e1e284c813a schema:volumeNumber 26
    41 rdf:type schema:PublicationVolume
    42 N756b820eb484432aa25b13a683d10904 schema:name doi
    43 schema:value 10.1007/bf01230421
    44 rdf:type schema:PropertyValue
    45 N7617b1af6a94480f9849aa92777e5264 rdf:first sg:person.07420122720.37
    46 rdf:rest rdf:nil
    47 Na3c8285654ad48c0ab2117140eaa1d3f schema:name dimensions_id
    48 schema:value pub.1002947958
    49 rdf:type schema:PropertyValue
    50 Ne5948fc0be08405497e1c45166d31cf8 schema:name readcube_id
    51 schema:value 0e0a3a6fbd3c58312b2e326b57a59207f1baffe16e80505c6cd481c37b6cf9e8
    52 rdf:type schema:PropertyValue
    53 Ne691b77c0cc94acf8553ad02a927a542 schema:issueNumber 4
    54 rdf:type schema:PublicationIssue
    55 Nf791907984e64b2a8e0bd73f806959ab schema:name Springer Nature - SN SciGraph project
    56 rdf:type schema:Organization
    57 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    58 schema:name Mathematical Sciences
    59 rdf:type schema:DefinedTerm
    60 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
    61 schema:name Applied Mathematics
    62 rdf:type schema:DefinedTerm
    63 sg:journal.1136436 schema:issn 0008-8714
    64 0923-2958
    65 schema:name Celestial Mechanics and Dynamical Astronomy
    66 rdf:type schema:Periodical
    67 sg:person.07420122720.37 schema:affiliation https://www.grid.ac/institutes/grid.10025.36
    68 schema:familyName Jupp
    69 schema:givenName A. H.
    70 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07420122720.37
    71 rdf:type schema:Person
    72 sg:pub.10.1007/bf01227802 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011827560
    73 https://doi.org/10.1007/bf01227802
    74 rdf:type schema:CreativeWork
    75 sg:pub.10.1007/bf01227819 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013346507
    76 https://doi.org/10.1007/bf01227819
    77 rdf:type schema:CreativeWork
    78 sg:pub.10.1007/bf01228388 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005645418
    79 https://doi.org/10.1007/bf01228388
    80 rdf:type schema:CreativeWork
    81 sg:pub.10.1007/bf01230167 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016607058
    82 https://doi.org/10.1007/bf01230167
    83 rdf:type schema:CreativeWork
    84 sg:pub.10.1007/bf01230455 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013280863
    85 https://doi.org/10.1007/bf01230455
    86 rdf:type schema:CreativeWork
    87 sg:pub.10.1007/bf01230629 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028918192
    88 https://doi.org/10.1007/bf01230629
    89 rdf:type schema:CreativeWork
    90 sg:pub.10.1007/bf01236167 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047634101
    91 https://doi.org/10.1007/bf01236167
    92 rdf:type schema:CreativeWork
    93 https://doi.org/10.1086/107956 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058446683
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.1086/107958 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058446685
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.1086/108248 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058446954
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.1086/110171 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058448772
    100 rdf:type schema:CreativeWork
    101 https://doi.org/10.1086/111099 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058449678
    102 rdf:type schema:CreativeWork
    103 https://doi.org/10.1093/mnras/148.2.197 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049777061
    104 rdf:type schema:CreativeWork
    105 https://www.grid.ac/institutes/grid.10025.36 schema:alternateName University of Liverpool
    106 schema:name Department of Applied Mathematics and Theoretical Physics, Liverpool University, England
    107 rdf:type schema:Organization
     




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


    ...