Stability of Motion Near Sun-Perturbed Earth-Moon Triangular Libration Points View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1970

AUTHORS

Ahmed A. Kamel , John V. Breakwell

ABSTRACT

An extension is presented of an analysis by Schechter [1] of sun-perturbed motion near the earth-moon L 4 point. In the present paper motion is confined to two dimensions. With the help of computerized symbolic manipulation and some new recurrence formulae [6] inspired by Deprit [4], a canonical perturbation treatment is carried to 4th order in the small quantities: lunar eccentricity, distance from L4/earth-moon distance, moon mass/earth mass, solar mean motion/lunar mean motion; (earth-moon distance/earth-sun distance) is included as a second order small quantity. Ignoring lunar eccentricity, stable one-month periodic orbits, synchronized with the sun, are found, from the 3rd-order Hamiltonian, somewhat larger than in Schechter’s second order treatment, and in very good agreement (3%) with Kolenkiewicz and Carpenter. Unstable three-month periodic orbits are also found in fairly close proximity to the stable one-month orbits, and the limited extent of the region of the stability is estimated in suitable phase coordinates. The inclusion of the 4th-order terms gave a slight deterioration rather than a further improvement in the agreement on the stable orbits. The inclusion of the lunar eccentricity up to 3rd-order yielded stable quasi-periodic orbits slightly larger than the previous stable orbits. More... »

PAGES

82-90

References to SciGraph publications

  • 1969-03. Canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1969-06. Expansion formulae in canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Book

    TITLE

    Periodic Orbits, Stability and Resonances

    ISBN

    978-94-010-3325-1
    978-94-010-3323-7

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-94-010-3323-7_8

    DOI

    http://dx.doi.org/10.1007/978-94-010-3323-7_8

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1025199245


    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/2008/0402", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Geochemistry", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/04", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Earth Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Stanford University", 
              "id": "https://www.grid.ac/institutes/grid.168010.e", 
              "name": [
                "Stanford University, Stanford, Calif., USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kamel", 
            "givenName": "Ahmed A.", 
            "id": "sg:person.013345305565.30", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013345305565.30"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Stanford University", 
              "id": "https://www.grid.ac/institutes/grid.168010.e", 
              "name": [
                "Stanford University, Stanford, Calif., USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Breakwell", 
            "givenName": "John V.", 
            "id": "sg:person.014463552077.01", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014463552077.01"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "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/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"
          }
        ], 
        "datePublished": "1970", 
        "datePublishedReg": "1970-01-01", 
        "description": "An extension is presented of an analysis by Schechter [1] of sun-perturbed motion near the earth-moon L 4 point. In the present paper motion is confined to two dimensions. With the help of computerized symbolic manipulation and some new recurrence formulae [6] inspired by Deprit [4], a canonical perturbation treatment is carried to 4th order in the small quantities: lunar eccentricity, distance from L4/earth-moon distance, moon mass/earth mass, solar mean motion/lunar mean motion; (earth-moon distance/earth-sun distance) is included as a second order small quantity. Ignoring lunar eccentricity, stable one-month periodic orbits, synchronized with the sun, are found, from the 3rd-order Hamiltonian, somewhat larger than in Schechter\u2019s second order treatment, and in very good agreement (3%) with Kolenkiewicz and Carpenter. Unstable three-month periodic orbits are also found in fairly close proximity to the stable one-month orbits, and the limited extent of the region of the stability is estimated in suitable phase coordinates. The inclusion of the 4th-order terms gave a slight deterioration rather than a further improvement in the agreement on the stable orbits. The inclusion of the lunar eccentricity up to 3rd-order yielded stable quasi-periodic orbits slightly larger than the previous stable orbits.", 
        "editor": [
          {
            "familyName": "Giacaglia", 
            "givenName": "G. E. O.", 
            "type": "Person"
          }
        ], 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/978-94-010-3323-7_8", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": {
          "isbn": [
            "978-94-010-3325-1", 
            "978-94-010-3323-7"
          ], 
          "name": "Periodic Orbits, Stability and Resonances", 
          "type": "Book"
        }, 
        "name": "Stability of Motion Near Sun-Perturbed Earth-Moon Triangular Libration Points", 
        "pagination": "82-90", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/978-94-010-3323-7_8"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "780c6fd49e70fd78757e9b70ee0d3324dcef42b8bc54c6833e07c298850594f0"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1025199245"
            ]
          }
        ], 
        "publisher": {
          "location": "Dordrecht", 
          "name": "Springer Netherlands", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/978-94-010-3323-7_8", 
          "https://app.dimensions.ai/details/publication/pub.1025199245"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-15T12:32", 
        "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_8663_00000258.jsonl", 
        "type": "Chapter", 
        "url": "http://link.springer.com/10.1007/978-94-010-3323-7_8"
      }
    ]
     

    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.10.1007/978-94-010-3323-7_8'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-94-010-3323-7_8'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-94-010-3323-7_8'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-94-010-3323-7_8'


     

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

    80 TRIPLES      23 PREDICATES      29 URIs      20 LITERALS      8 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/978-94-010-3323-7_8 schema:about anzsrc-for:04
    2 anzsrc-for:0402
    3 schema:author Nfb8d73827b7a4ad7aaa2630173558f75
    4 schema:citation sg:pub.10.1007/bf01228838
    5 sg:pub.10.1007/bf01230629
    6 schema:datePublished 1970
    7 schema:datePublishedReg 1970-01-01
    8 schema:description An extension is presented of an analysis by Schechter [1] of sun-perturbed motion near the earth-moon L 4 point. In the present paper motion is confined to two dimensions. With the help of computerized symbolic manipulation and some new recurrence formulae [6] inspired by Deprit [4], a canonical perturbation treatment is carried to 4th order in the small quantities: lunar eccentricity, distance from L4/earth-moon distance, moon mass/earth mass, solar mean motion/lunar mean motion; (earth-moon distance/earth-sun distance) is included as a second order small quantity. Ignoring lunar eccentricity, stable one-month periodic orbits, synchronized with the sun, are found, from the 3rd-order Hamiltonian, somewhat larger than in Schechter’s second order treatment, and in very good agreement (3%) with Kolenkiewicz and Carpenter. Unstable three-month periodic orbits are also found in fairly close proximity to the stable one-month orbits, and the limited extent of the region of the stability is estimated in suitable phase coordinates. The inclusion of the 4th-order terms gave a slight deterioration rather than a further improvement in the agreement on the stable orbits. The inclusion of the lunar eccentricity up to 3rd-order yielded stable quasi-periodic orbits slightly larger than the previous stable orbits.
    9 schema:editor N8caa1a3a9d4a4aeb86ebec7d2ca345f3
    10 schema:genre chapter
    11 schema:inLanguage en
    12 schema:isAccessibleForFree false
    13 schema:isPartOf Nb606864a0f6642898d88196fe37bffd1
    14 schema:name Stability of Motion Near Sun-Perturbed Earth-Moon Triangular Libration Points
    15 schema:pagination 82-90
    16 schema:productId Nbdb58050df8448e69bdcd7447712f3f4
    17 Nf53a9dfd0e974f9297448c0d711f1ee0
    18 Nfeda4661aba043ccadff19f99e9c22c2
    19 schema:publisher N5329f6535d584c869dac99af6ba8f83f
    20 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025199245
    21 https://doi.org/10.1007/978-94-010-3323-7_8
    22 schema:sdDatePublished 2019-04-15T12:32
    23 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    24 schema:sdPublisher N35af90d997d14257a7c3b4f32599c785
    25 schema:url http://link.springer.com/10.1007/978-94-010-3323-7_8
    26 sgo:license sg:explorer/license/
    27 sgo:sdDataset chapters
    28 rdf:type schema:Chapter
    29 N35af90d997d14257a7c3b4f32599c785 schema:name Springer Nature - SN SciGraph project
    30 rdf:type schema:Organization
    31 N3e4c9a393f47454fa84ce8e349fe417d schema:familyName Giacaglia
    32 schema:givenName G. E. O.
    33 rdf:type schema:Person
    34 N5329f6535d584c869dac99af6ba8f83f schema:location Dordrecht
    35 schema:name Springer Netherlands
    36 rdf:type schema:Organisation
    37 N8caa1a3a9d4a4aeb86ebec7d2ca345f3 rdf:first N3e4c9a393f47454fa84ce8e349fe417d
    38 rdf:rest rdf:nil
    39 Nb606864a0f6642898d88196fe37bffd1 schema:isbn 978-94-010-3323-7
    40 978-94-010-3325-1
    41 schema:name Periodic Orbits, Stability and Resonances
    42 rdf:type schema:Book
    43 Nbdb58050df8448e69bdcd7447712f3f4 schema:name dimensions_id
    44 schema:value pub.1025199245
    45 rdf:type schema:PropertyValue
    46 Nefcd4845ec0b4d81bccd5eb1bdcfb22a rdf:first sg:person.014463552077.01
    47 rdf:rest rdf:nil
    48 Nf53a9dfd0e974f9297448c0d711f1ee0 schema:name readcube_id
    49 schema:value 780c6fd49e70fd78757e9b70ee0d3324dcef42b8bc54c6833e07c298850594f0
    50 rdf:type schema:PropertyValue
    51 Nfb8d73827b7a4ad7aaa2630173558f75 rdf:first sg:person.013345305565.30
    52 rdf:rest Nefcd4845ec0b4d81bccd5eb1bdcfb22a
    53 Nfeda4661aba043ccadff19f99e9c22c2 schema:name doi
    54 schema:value 10.1007/978-94-010-3323-7_8
    55 rdf:type schema:PropertyValue
    56 anzsrc-for:04 schema:inDefinedTermSet anzsrc-for:
    57 schema:name Earth Sciences
    58 rdf:type schema:DefinedTerm
    59 anzsrc-for:0402 schema:inDefinedTermSet anzsrc-for:
    60 schema:name Geochemistry
    61 rdf:type schema:DefinedTerm
    62 sg:person.013345305565.30 schema:affiliation https://www.grid.ac/institutes/grid.168010.e
    63 schema:familyName Kamel
    64 schema:givenName Ahmed A.
    65 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013345305565.30
    66 rdf:type schema:Person
    67 sg:person.014463552077.01 schema:affiliation https://www.grid.ac/institutes/grid.168010.e
    68 schema:familyName Breakwell
    69 schema:givenName John V.
    70 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014463552077.01
    71 rdf:type schema:Person
    72 sg:pub.10.1007/bf01228838 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042537547
    73 https://doi.org/10.1007/bf01228838
    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://www.grid.ac/institutes/grid.168010.e schema:alternateName Stanford University
    79 schema:name Stanford University, Stanford, Calif., USA
    80 rdf:type schema:Organization
     




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


    ...