On a Convex Embedding of the Euler Problem of Two Fixed Centers View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-05

AUTHORS

Seongchan Kim

ABSTRACT

In this article, we study a convex embedding for the Euler problem of two fixed centers for energies below the critical energy level. We prove that the doubly-covered elliptic coordinates provide a 2-to-1 symplectic embedding such that the image of the bounded component near the lighter primary of the regularized Euler problem is convex for any energy below the critical Jacobi energy. This holds true if the two primaries have equal mass, but does not hold near the heavier body. More... »

PAGES

304-324

References to SciGraph publications

  • 2004-09. Convex energy levels of Hamiltonian systems in QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
  • 1993-12. Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three in INVENTIONES MATHEMATICAE
  • 1912-12. Sur un théorème de géométrie in RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO SERIES 1
  • 1920-12. Sur la régularisation du problème des trois corps in ACTA MATHEMATICA
  • 2011-10-27. Global Surfaces of Section in the Planar Restricted 3-Body Problem in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1915-12. The restricted problem of three bodies in RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO SERIES 1
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1134/s1560354718030061

    DOI

    http://dx.doi.org/10.1134/s1560354718030061

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1104420676


    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"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0105", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Physics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Mathematisches Institut, Universit\u00e4t Augsburg, Universit\u00e4tsstrasse 14, 86159, Augsburg, Germany", 
              "id": "http://www.grid.ac/institutes/grid.7307.3", 
              "name": [
                "Mathematisches Institut, Universit\u00e4t Augsburg, Universit\u00e4tsstrasse 14, 86159, Augsburg, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kim", 
            "givenName": "Seongchan", 
            "id": "sg:person.012334350464.55", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012334350464.55"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s00205-011-0475-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010283364", 
              "https://doi.org/10.1007/s00205-011-0475-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01232679", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039383225", 
              "https://doi.org/10.1007/bf01232679"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02404404", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027431063", 
              "https://doi.org/10.1007/bf02404404"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf03015314", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027291129", 
              "https://doi.org/10.1007/bf03015314"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf03015982", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018541218", 
              "https://doi.org/10.1007/bf03015982"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02970869", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010424875", 
              "https://doi.org/10.1007/bf02970869"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2018-05", 
        "datePublishedReg": "2018-05-01", 
        "description": "In this article, we study a convex embedding for the Euler problem of two fixed centers for energies below the critical energy level. We prove that the doubly-covered elliptic coordinates provide a 2-to-1 symplectic embedding such that the image of the bounded component near the lighter primary of the regularized Euler problem is convex for any energy below the critical Jacobi energy. This holds true if the two primaries have equal mass, but does not hold near the heavier body.", 
        "genre": "article", 
        "id": "sg:pub.10.1134/s1560354718030061", 
        "inLanguage": "en", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136573", 
            "issn": [
              "1468-4845", 
              "1560-3547"
            ], 
            "name": "Regular and Chaotic Dynamics", 
            "publisher": "Pleiades Publishing", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "23"
          }
        ], 
        "keywords": [
          "primary", 
          "center", 
          "levels", 
          "body", 
          "mass", 
          "heavy body", 
          "article", 
          "components", 
          "problem", 
          "images", 
          "energy", 
          "critical energy level", 
          "symplectic embedding", 
          "convex embedding", 
          "Euler problem", 
          "energy levels", 
          "Jacobi energy", 
          "embedding", 
          "elliptic coordinates", 
          "light primaries", 
          "equal mass", 
          "coordinates", 
          "critical Jacobi energy", 
          "Fixed Centers"
        ], 
        "name": "On a Convex Embedding of the Euler Problem of Two Fixed Centers", 
        "pagination": "304-324", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1104420676"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1134/s1560354718030061"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1134/s1560354718030061", 
          "https://app.dimensions.ai/details/publication/pub.1104420676"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2021-12-01T19:40", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20211201/entities/gbq_results/article/article_761.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1134/s1560354718030061"
      }
    ]
     

    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.10.1134/s1560354718030061'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1134/s1560354718030061'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1134/s1560354718030061'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1134/s1560354718030061'


     

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

    110 TRIPLES      22 PREDICATES      56 URIs      41 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1134/s1560354718030061 schema:about anzsrc-for:01
    2 anzsrc-for:0102
    3 anzsrc-for:0105
    4 schema:author Nb1db56d22a524975a9628c2e79734b55
    5 schema:citation sg:pub.10.1007/bf01232679
    6 sg:pub.10.1007/bf02404404
    7 sg:pub.10.1007/bf02970869
    8 sg:pub.10.1007/bf03015314
    9 sg:pub.10.1007/bf03015982
    10 sg:pub.10.1007/s00205-011-0475-2
    11 schema:datePublished 2018-05
    12 schema:datePublishedReg 2018-05-01
    13 schema:description In this article, we study a convex embedding for the Euler problem of two fixed centers for energies below the critical energy level. We prove that the doubly-covered elliptic coordinates provide a 2-to-1 symplectic embedding such that the image of the bounded component near the lighter primary of the regularized Euler problem is convex for any energy below the critical Jacobi energy. This holds true if the two primaries have equal mass, but does not hold near the heavier body.
    14 schema:genre article
    15 schema:inLanguage en
    16 schema:isAccessibleForFree true
    17 schema:isPartOf Na9fb59a83b2f4cc2aea29e1056ae0eaa
    18 Nd4b54c920ad0490e852956fe7920a0f8
    19 sg:journal.1136573
    20 schema:keywords Euler problem
    21 Fixed Centers
    22 Jacobi energy
    23 article
    24 body
    25 center
    26 components
    27 convex embedding
    28 coordinates
    29 critical Jacobi energy
    30 critical energy level
    31 elliptic coordinates
    32 embedding
    33 energy
    34 energy levels
    35 equal mass
    36 heavy body
    37 images
    38 levels
    39 light primaries
    40 mass
    41 primary
    42 problem
    43 symplectic embedding
    44 schema:name On a Convex Embedding of the Euler Problem of Two Fixed Centers
    45 schema:pagination 304-324
    46 schema:productId N1f5941f80f2f451ba526cc9afabf499d
    47 Nb62dfdbcc9ec436eb0248bf11ba1f45b
    48 schema:sameAs https://app.dimensions.ai/details/publication/pub.1104420676
    49 https://doi.org/10.1134/s1560354718030061
    50 schema:sdDatePublished 2021-12-01T19:40
    51 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    52 schema:sdPublisher N8dee81eded5f43e594c62cd986e0d425
    53 schema:url https://doi.org/10.1134/s1560354718030061
    54 sgo:license sg:explorer/license/
    55 sgo:sdDataset articles
    56 rdf:type schema:ScholarlyArticle
    57 N1f5941f80f2f451ba526cc9afabf499d schema:name dimensions_id
    58 schema:value pub.1104420676
    59 rdf:type schema:PropertyValue
    60 N8dee81eded5f43e594c62cd986e0d425 schema:name Springer Nature - SN SciGraph project
    61 rdf:type schema:Organization
    62 Na9fb59a83b2f4cc2aea29e1056ae0eaa schema:issueNumber 3
    63 rdf:type schema:PublicationIssue
    64 Nb1db56d22a524975a9628c2e79734b55 rdf:first sg:person.012334350464.55
    65 rdf:rest rdf:nil
    66 Nb62dfdbcc9ec436eb0248bf11ba1f45b schema:name doi
    67 schema:value 10.1134/s1560354718030061
    68 rdf:type schema:PropertyValue
    69 Nd4b54c920ad0490e852956fe7920a0f8 schema:volumeNumber 23
    70 rdf:type schema:PublicationVolume
    71 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    72 schema:name Mathematical Sciences
    73 rdf:type schema:DefinedTerm
    74 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
    75 schema:name Applied Mathematics
    76 rdf:type schema:DefinedTerm
    77 anzsrc-for:0105 schema:inDefinedTermSet anzsrc-for:
    78 schema:name Mathematical Physics
    79 rdf:type schema:DefinedTerm
    80 sg:journal.1136573 schema:issn 1468-4845
    81 1560-3547
    82 schema:name Regular and Chaotic Dynamics
    83 schema:publisher Pleiades Publishing
    84 rdf:type schema:Periodical
    85 sg:person.012334350464.55 schema:affiliation grid-institutes:grid.7307.3
    86 schema:familyName Kim
    87 schema:givenName Seongchan
    88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012334350464.55
    89 rdf:type schema:Person
    90 sg:pub.10.1007/bf01232679 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039383225
    91 https://doi.org/10.1007/bf01232679
    92 rdf:type schema:CreativeWork
    93 sg:pub.10.1007/bf02404404 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027431063
    94 https://doi.org/10.1007/bf02404404
    95 rdf:type schema:CreativeWork
    96 sg:pub.10.1007/bf02970869 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010424875
    97 https://doi.org/10.1007/bf02970869
    98 rdf:type schema:CreativeWork
    99 sg:pub.10.1007/bf03015314 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027291129
    100 https://doi.org/10.1007/bf03015314
    101 rdf:type schema:CreativeWork
    102 sg:pub.10.1007/bf03015982 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018541218
    103 https://doi.org/10.1007/bf03015982
    104 rdf:type schema:CreativeWork
    105 sg:pub.10.1007/s00205-011-0475-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010283364
    106 https://doi.org/10.1007/s00205-011-0475-2
    107 rdf:type schema:CreativeWork
    108 grid-institutes:grid.7307.3 schema:alternateName Mathematisches Institut, Universität Augsburg, Universitätsstrasse 14, 86159, Augsburg, Germany
    109 schema:name Mathematisches Institut, Universität Augsburg, Universitätsstrasse 14, 86159, Augsburg, Germany
    110 rdf:type schema:Organization
     




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


    ...