{"id":"https://openalex.org/W4391576559","doi":"https://doi.org/10.3390/a17020066","title":"A Geometrical Study about the Biparametric Family of Anomalies in the Elliptic Two-Body Problem with Extensions to Other Families","display_name":"A Geometrical Study about the Biparametric Family of Anomalies in the Elliptic Two-Body Problem with Extensions to Other Families","publication_year":2024,"publication_date":"2024-02-04","ids":{"openalex":"https://openalex.org/W4391576559","doi":"https://doi.org/10.3390/a17020066"},"language":"en","primary_location":{"id":"doi:10.3390/a17020066","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17020066","pdf_url":"https://www.mdpi.com/1999-4893/17/2/66/pdf?version=1707033121","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/17/2/66/pdf?version=1707033121","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062414108","display_name":"Jos\u00e9 Antonio L\u00f3pez Ort\u00ed","orcid":"https://orcid.org/0000-0002-9620-6454"},"institutions":[{"id":"https://openalex.org/I10902133","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11","country_code":"ES","type":"education","lineage":["https://openalex.org/I10902133"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 Antonio L\u00f3pez Ort\u00ed","raw_affiliation_strings":["Department of Mathematics, IMAC, Universitat Jaume I de Castell\u00f3n, E-12071 Castell\u00f3n, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9620-6454","affiliations":[{"raw_affiliation_string":"Department of Mathematics, IMAC, Universitat Jaume I de Castell\u00f3n, E-12071 Castell\u00f3n, Spain","institution_ids":["https://openalex.org/I10902133"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101451759","display_name":"F. J. Marco","orcid":"https://orcid.org/0000-0001-9866-7601"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Francisco Jos\u00e9 Marco Castillo","raw_affiliation_strings":["Department of Applied Mathematics, IUMPA, Universitat Polit\u00e8cnica de Val\u00e8ncia, E-46022 Valencia, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9866-7601","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, IUMPA, Universitat Polit\u00e8cnica de Val\u00e8ncia, E-46022 Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078678069","display_name":"Mar\u00eda Jos\u00e9 Mart\u00ednez Mart\u00ednez","orcid":"https://orcid.org/0000-0002-9230-521X"},"institutions":[{"id":"https://openalex.org/I10902133","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11","country_code":"ES","type":"education","lineage":["https://openalex.org/I10902133"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mar\u00eda Jos\u00e9 Mart\u00ednez Us\u00f3","raw_affiliation_strings":["Department of Mathematics, IMAC, Universitat Jaume I de Castell\u00f3n, E-12071 Castell\u00f3n, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9230-521X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, IMAC, Universitat Jaume I de Castell\u00f3n, E-12071 Castell\u00f3n, Spain","institution_ids":["https://openalex.org/I10902133"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062414108"],"corresponding_institution_ids":["https://openalex.org/I10902133"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01425081,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"2","first_page":"66","last_page":"66"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10325","display_name":"Astro and Planetary Science","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10039","display_name":"Stellar, planetary, and galactic studies","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ellipsoid","display_name":"Ellipsoid","score":0.6854857802391052},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5717065930366516},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.5340204834938049},{"id":"https://openalex.org/keywords/anomaly","display_name":"Anomaly (physics)","score":0.46212291717529297},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45022648572921753},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4374188780784607},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.42397499084472656},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.355988472700119},{"id":"https://openalex.org/keywords/geodesy","display_name":"Geodesy","score":0.3233368992805481},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3116230368614197},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27357611060142517},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24437585473060608},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.2111302614212036}],"concepts":[{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.6854857802391052},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5717065930366516},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.5340204834938049},{"id":"https://openalex.org/C12997251","wikidata":"https://www.wikidata.org/wiki/Q567560","display_name":"Anomaly (physics)","level":2,"score":0.46212291717529297},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45022648572921753},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4374188780784607},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.42397499084472656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.355988472700119},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.3233368992805481},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3116230368614197},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27357611060142517},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24437585473060608},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.2111302614212036},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/a17020066","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17020066","pdf_url":"https://www.mdpi.com/1999-4893/17/2/66/pdf?version=1707033121","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:riunet.upv.es:10251/210323","is_oa":true,"landing_page_url":"http://hdl.handle.net/10251/210323","pdf_url":"https://riunet.upv.es/bitstreams/b991b3d5-6be3-4f83-8a8e-3c02c0fee3de/download","source":{"id":"https://openalex.org/S4306401646","display_name":"Repositorio Institucional de la Universitat Polit\u00e8cnica (Universitat Polit\u00e8cnica de Val\u00e8ncia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60053951","host_organization_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","host_organization_lineage":["https://openalex.org/I60053951"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:415f90b0739f40a5a03cf98d5e9c0ae5","is_oa":false,"landing_page_url":"https://doaj.org/article/415f90b0739f40a5a03cf98d5e9c0ae5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 17, Iss 2, p 66 (2024)","raw_type":"article"},{"id":"pmh:oai:repositori.uji.es:10234/206093","is_oa":true,"landing_page_url":"http://hdl.handle.net/10234/206093","pdf_url":null,"source":{"id":"https://openalex.org/S4306400303","display_name":"Repositori UJI (Universitat Jaume I)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I10902133","host_organization_name":"Universitat Jaume I","host_organization_lineage":["https://openalex.org/I10902133"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/a17020066","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17020066","pdf_url":"https://www.mdpi.com/1999-4893/17/2/66/pdf?version=1707033121","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G289169882","display_name":null,"funder_award_id":"16I358.01/1","funder_id":"https://openalex.org/F4320322926","funder_display_name":"Universitat Jaume I"}],"funders":[{"id":"https://openalex.org/F4320322926","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391576559.pdf","grobid_xml":"https://content.openalex.org/works/W4391576559.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1971842540","https://openalex.org/W1973177040","https://openalex.org/W2015842644","https://openalex.org/W2024737582","https://openalex.org/W2036130654","https://openalex.org/W2074488013","https://openalex.org/W2087784594","https://openalex.org/W2088089549","https://openalex.org/W2276212217","https://openalex.org/W2297246647","https://openalex.org/W2313721366","https://openalex.org/W3048327118","https://openalex.org/W4212809178","https://openalex.org/W4286504960"],"related_works":["https://openalex.org/W2005485125","https://openalex.org/W2390718407","https://openalex.org/W1986006778","https://openalex.org/W2034124193","https://openalex.org/W2379017606","https://openalex.org/W4211143546","https://openalex.org/W2171970890","https://openalex.org/W2356423988","https://openalex.org/W2156319555","https://openalex.org/W2388969307"],"abstract_inverted_index":{"In":[0,34,76],"the":[1,7,25,30,52,56,77,82,90,95,108,111,115,118,121,124,127,132,137,141,148,169,176,185,192,202,209],"present":[2,78],"paper,":[3],"we":[4,37,80],"efficiently":[5],"solve":[6],"two-body":[8],"problem":[9,42],"for":[10],"extreme":[11],"cases":[12],"such":[13],"as":[14,85],"those":[15],"with":[16,24,64],"high":[17],"eccentricities.":[18],"The":[19,59,153,188],"use":[20],"of":[21,62,73,89,92,107,114,134,184,201,204,211],"numerical":[22],"methods,":[23],"usual":[26],"variables,":[27],"cannot":[28],"maintain":[29],"perihelion":[31],"passage":[32],"accurately.":[33],"previous":[35],"articles,":[36],"have":[38],"verified":[39],"that":[40],"this":[41],"is":[43,110,123,174],"treated":[44],"more":[45],"adequately":[46],"through":[47,55],"temporal":[48],"reparametrizations":[49,206],"related":[50],"to":[51,103,126,168],"mean":[53,112],"anomaly":[54],"partition":[57,67,96],"function.":[58],"biparametric":[60,170,186],"family":[61],"anomalies,":[63],"an":[65,182],"appropriate":[66],"function,":[68],"allows":[69],"a":[70,86,144,198],"systematic":[71],"study":[72,210],"these":[74],"transformations.":[75],"work,":[79],"consider":[81],"elliptical":[83],"orbit":[84],"meridian":[87],"section":[88],"ellipsoid":[91,116],"revolution,":[93],"and":[94,120,140,150],"function":[97],"depends":[98],"on":[99],"two":[100],"variables":[101,109,159],"raised":[102],"specific":[104],"parameters.":[105],"One":[106,129],"radius":[113],"at":[117],"secondary,":[119],"other":[122,142],"distance":[125],"primary.":[128],"parameter":[130],"regulates":[131],"concentration":[133],"points":[135],"in":[136,164,175,208],"apoapsis":[138],"region,":[139],"produces":[143],"symmetrical":[145],"displacement":[146],"between":[147],"polar":[149],"equatorial":[151],"regions.":[152],"three":[154],"most":[155],"used":[156,207],"geodesy":[157],"latitude":[158],"are":[160],"also":[161],"studied,":[162],"resulting":[163],"one":[165,177],"not":[166],"belonging":[167],"family.":[171],"However,":[172],"it":[173],"introduced":[178],"now,":[179],"which":[180],"implies":[181],"extension":[183],"method.":[187],"results":[189],"obtained":[190],"using":[191],"method":[193],"presented":[194],"here":[195],"now":[196],"allow":[197],"causal":[199],"interpretation":[200],"operation":[203],"numerous":[205],"orbital":[212],"motion.":[213]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2024-02-07T00:00:00"}
