On a perturbation theory using Lie transforms View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1970-03

AUTHORS

Jacques Henrard

ABSTRACT

Kamel has recently extended to non-Hamiltonian equations a perturbation theory using Lie transforms. We show here how Kamel's extension can be approached from an intrinsic viewpoint, which reformulation leads to a simpler algorithm. Then we complete Kamel's contribution by establishing the rules for inverting the transformation generated by the perturbation theory, and for composing two such transformations. More... »

PAGES

107-120

References to SciGraph publications

  • 1969-03. Canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1969-06. Birkhoff's normalization in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970-03. Perturbation method in the theory of nonlinear oscillations in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1969-06. Expansion formulae in canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01230436

    DOI

    http://dx.doi.org/10.1007/bf01230436

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1013740596


    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/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure 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": {
              "name": [
                "Mathematics Research Laboratory, Boeing Scientific Research Laboratories, Seattle, Wash., U.S.A."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Henrard", 
            "givenName": "Jacques", 
            "id": "sg:person.07540542307.45", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07540542307.45"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01230435", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016915999", 
              "https://doi.org/10.1007/bf01230435"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01230435", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016915999", 
              "https://doi.org/10.1007/bf01230435"
            ], 
            "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/bf01228842", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030762838", 
              "https://doi.org/10.1007/bf01228842"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01228842", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030762838", 
              "https://doi.org/10.1007/bf01228842"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01228838", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042537547", 
              "https://doi.org/10.1007/bf01228838"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01228838", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042537547", 
              "https://doi.org/10.1007/bf01228838"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/1969262", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069674653"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1970-03", 
        "datePublishedReg": "1970-03-01", 
        "description": "Kamel has recently extended to non-Hamiltonian equations a perturbation theory using Lie transforms. We show here how Kamel's extension can be approached from an intrinsic viewpoint, which reformulation leads to a simpler algorithm. Then we complete Kamel's contribution by establishing the rules for inverting the transformation generated by the perturbation theory, and for composing two such transformations.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/bf01230436", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136436", 
            "issn": [
              "0008-8714", 
              "0923-2958"
            ], 
            "name": "Celestial Mechanics and Dynamical Astronomy", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "3"
          }
        ], 
        "name": "On a perturbation theory using Lie transforms", 
        "pagination": "107-120", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "41753423763f4137e935ae5dfa2d696975128b60c4d6a410e897ccc82b03bc52"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf01230436"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1013740596"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf01230436", 
          "https://app.dimensions.ai/details/publication/pub.1013740596"
        ], 
        "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/BF01230436"
      }
    ]
     

    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/bf01230436'

    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/bf01230436'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01230436'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01230436'


     

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

    79 TRIPLES      21 PREDICATES      32 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf01230436 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Ndfe2f1bdcc624e1d8468b776fe77bdcc
    4 schema:citation sg:pub.10.1007/bf01228838
    5 sg:pub.10.1007/bf01228842
    6 sg:pub.10.1007/bf01230435
    7 sg:pub.10.1007/bf01230629
    8 https://doi.org/10.2307/1969262
    9 schema:datePublished 1970-03
    10 schema:datePublishedReg 1970-03-01
    11 schema:description Kamel has recently extended to non-Hamiltonian equations a perturbation theory using Lie transforms. We show here how Kamel's extension can be approached from an intrinsic viewpoint, which reformulation leads to a simpler algorithm. Then we complete Kamel's contribution by establishing the rules for inverting the transformation generated by the perturbation theory, and for composing two such transformations.
    12 schema:genre research_article
    13 schema:inLanguage en
    14 schema:isAccessibleForFree false
    15 schema:isPartOf N11994c8052b94cf8930c150278e7da0d
    16 Ncefcb5379ec44f4f9629b9495480c725
    17 sg:journal.1136436
    18 schema:name On a perturbation theory using Lie transforms
    19 schema:pagination 107-120
    20 schema:productId N02028bd158f94b7eb4464e5ba4d0618f
    21 N07329039e0b240c3ba13cfceea4a1105
    22 Nd90980760aac4602a71fdb54575ccedc
    23 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013740596
    24 https://doi.org/10.1007/bf01230436
    25 schema:sdDatePublished 2019-04-11T13:29
    26 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    27 schema:sdPublisher Nd8da399fe741416c99bf5c83eda65585
    28 schema:url http://link.springer.com/10.1007/BF01230436
    29 sgo:license sg:explorer/license/
    30 sgo:sdDataset articles
    31 rdf:type schema:ScholarlyArticle
    32 N02028bd158f94b7eb4464e5ba4d0618f schema:name readcube_id
    33 schema:value 41753423763f4137e935ae5dfa2d696975128b60c4d6a410e897ccc82b03bc52
    34 rdf:type schema:PropertyValue
    35 N07329039e0b240c3ba13cfceea4a1105 schema:name dimensions_id
    36 schema:value pub.1013740596
    37 rdf:type schema:PropertyValue
    38 N11994c8052b94cf8930c150278e7da0d schema:issueNumber 1
    39 rdf:type schema:PublicationIssue
    40 Nb7b7ddcb6d4a4d0cb6a3b7047ebb1f96 schema:name Mathematics Research Laboratory, Boeing Scientific Research Laboratories, Seattle, Wash., U.S.A.
    41 rdf:type schema:Organization
    42 Ncefcb5379ec44f4f9629b9495480c725 schema:volumeNumber 3
    43 rdf:type schema:PublicationVolume
    44 Nd8da399fe741416c99bf5c83eda65585 schema:name Springer Nature - SN SciGraph project
    45 rdf:type schema:Organization
    46 Nd90980760aac4602a71fdb54575ccedc schema:name doi
    47 schema:value 10.1007/bf01230436
    48 rdf:type schema:PropertyValue
    49 Ndfe2f1bdcc624e1d8468b776fe77bdcc rdf:first sg:person.07540542307.45
    50 rdf:rest rdf:nil
    51 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    52 schema:name Mathematical Sciences
    53 rdf:type schema:DefinedTerm
    54 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    55 schema:name Pure Mathematics
    56 rdf:type schema:DefinedTerm
    57 sg:journal.1136436 schema:issn 0008-8714
    58 0923-2958
    59 schema:name Celestial Mechanics and Dynamical Astronomy
    60 rdf:type schema:Periodical
    61 sg:person.07540542307.45 schema:affiliation Nb7b7ddcb6d4a4d0cb6a3b7047ebb1f96
    62 schema:familyName Henrard
    63 schema:givenName Jacques
    64 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07540542307.45
    65 rdf:type schema:Person
    66 sg:pub.10.1007/bf01228838 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042537547
    67 https://doi.org/10.1007/bf01228838
    68 rdf:type schema:CreativeWork
    69 sg:pub.10.1007/bf01228842 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030762838
    70 https://doi.org/10.1007/bf01228842
    71 rdf:type schema:CreativeWork
    72 sg:pub.10.1007/bf01230435 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016915999
    73 https://doi.org/10.1007/bf01230435
    74 rdf:type schema:CreativeWork
    75 sg:pub.10.1007/bf01230629 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028918192
    76 https://doi.org/10.1007/bf01230629
    77 rdf:type schema:CreativeWork
    78 https://doi.org/10.2307/1969262 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069674653
    79 rdf:type schema:CreativeWork
     




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


    ...