{"id":"https://openalex.org/W2935861007","doi":"https://doi.org/10.1137/18m1178852","title":"Application of Topological Degree Theory to the Equilibrium Point in Irregular Gravitational Field","display_name":"Application of Topological Degree Theory to the Equilibrium Point in Irregular Gravitational Field","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2935861007","doi":"https://doi.org/10.1137/18m1178852","mag":"2935861007"},"language":"en","primary_location":{"id":"doi:10.1137/18m1178852","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1178852","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100778529","display_name":"Hao Sun","orcid":"https://orcid.org/0000-0003-0951-6428"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hao Sun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100450056","display_name":"Junfeng Li","orcid":"https://orcid.org/0000-0002-5356-3478"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Junfeng Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02449947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"2","first_page":"629","last_page":"642"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10325","display_name":"Astro and Planetary Science","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10325","display_name":"Astro and Planetary Science","score":0.9998000264167786,"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":0.9975000023841858,"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/T10406","display_name":"Planetary Science and Exploration","score":0.9957000017166138,"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/gravitational-field","display_name":"Gravitational field","score":0.7237032651901245},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6447263956069946},{"id":"https://openalex.org/keywords/gravitation","display_name":"Gravitation","score":0.6189118027687073},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.5596524477005005},{"id":"https://openalex.org/keywords/celestial-mechanics","display_name":"Celestial mechanics","score":0.5082201957702637},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5072957873344421},{"id":"https://openalex.org/keywords/gravitational-potential","display_name":"Gravitational potential","score":0.5066681504249573},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.4842336177825928},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4401700794696808},{"id":"https://openalex.org/keywords/coordinate-system","display_name":"Coordinate system","score":0.4365385174751282},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3407822847366333},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2826799750328064},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25201302766799927},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10794314742088318},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10668495297431946},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10307967662811279}],"concepts":[{"id":"https://openalex.org/C14257148","wikidata":"https://www.wikidata.org/wiki/Q558066","display_name":"Gravitational field","level":2,"score":0.7237032651901245},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6447263956069946},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.6189118027687073},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.5596524477005005},{"id":"https://openalex.org/C27638517","wikidata":"https://www.wikidata.org/wiki/Q184274","display_name":"Celestial mechanics","level":2,"score":0.5082201957702637},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5072957873344421},{"id":"https://openalex.org/C127090403","wikidata":"https://www.wikidata.org/wiki/Q1544012","display_name":"Gravitational potential","level":3,"score":0.5066681504249573},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.4842336177825928},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4401700794696808},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.4365385174751282},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3407822847366333},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2826799750328064},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25201302766799927},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10794314742088318},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10668495297431946},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10307967662811279},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1178852","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1178852","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1035309434","display_name":null,"funder_award_id":"11872223","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7061813319","display_name":null,"funder_award_id":"11871299","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1507967549","https://openalex.org/W1948602830","https://openalex.org/W1973010492","https://openalex.org/W1990111190","https://openalex.org/W2064506310","https://openalex.org/W2070164090","https://openalex.org/W2092750091","https://openalex.org/W2099447630","https://openalex.org/W2126417924","https://openalex.org/W3103568148","https://openalex.org/W3105308280"],"related_works":["https://openalex.org/W2742829666","https://openalex.org/W2157132090","https://openalex.org/W4237425780","https://openalex.org/W205084862","https://openalex.org/W3177867369","https://openalex.org/W3195368265","https://openalex.org/W2988506060","https://openalex.org/W4321489929","https://openalex.org/W2340109481","https://openalex.org/W1981486729"],"abstract_inverted_index":{"The":[0,15,122],"equilibrium":[1,22,63,97],"point":[2],"in":[3,24,69,99],"an":[4,25],"irregular":[5,26,85,101],"gravitational":[6,27,86,102],"field":[7,28,68,87],"has":[8],"been":[9],"a":[10,75],"focus":[11],"of":[12,21,33,38,57,65,74,96,107,115],"recent":[13],"research.":[14],"numerical":[16,141],"results":[17,82,149],"indicated":[18],"the":[19,34,39,45,51,62,66,70,81,84,89,100,108,116,128,134,145,148],"number":[20],"points":[23,64,98],"is":[29],"always":[30],"odd,":[31],"regardless":[32],"shape":[35],"or":[36,112],"density":[37,113],"celestial":[40,117,130],"body.":[41],"This":[42],"article":[43],"applies":[44],"topological":[46],"degree":[47],"theory":[48,53],"and":[49,54,79,147],"demonstrates":[50],"mathematical":[52],"physical":[55],"mechanism":[56],"this":[58],"phenomenon.":[59],"We":[60,92],"study":[61],"force":[67],"fixed":[71],"coordinate":[72],"system":[73],"rotating":[76],"homogeneous":[77],"ball":[78],"generalize":[80],"to":[83,127,143],"by":[88],"homotopy":[90],"method.":[91],"demonstrate":[93],"intrinsic":[94],"properties":[95],"field,":[103],"which":[104],"are":[105,124,138],"independent":[106],"shape,":[109],"angular":[110],"velocity,":[111],"distribution":[114],"body":[118],"under":[119],"certain":[120],"assumptions.":[121],"conclusions":[123],"also":[125],"extended":[126],"multiple":[129],"bodies":[131],"system.":[132],"In":[133],"end,":[135],"real":[136],"asteroids":[137],"used":[139],"as":[140],"examples":[142],"verify":[144],"conclusions,":[146],"agree":[150],"well":[151],"with":[152],"our":[153],"analysis.":[154]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}