{"id":"https://openalex.org/W3206234918","doi":"https://doi.org/10.29235/1561-2430-2021-57-3-330-346","title":"\u03c1-Libration point in the three body problem","display_name":"\u03c1-Libration point in the three body problem","publication_year":2021,"publication_date":"2021-10-07","ids":{"openalex":"https://openalex.org/W3206234918","doi":"https://doi.org/10.29235/1561-2430-2021-57-3-330-346","mag":"3206234918"},"language":"en","primary_location":{"id":"doi:10.29235/1561-2430-2021-57-3-330-346","doi":"https://doi.org/10.29235/1561-2430-2021-57-3-330-346","is_oa":true,"landing_page_url":"https://doi.org/10.29235/1561-2430-2021-57-3-330-346","pdf_url":"https://vestifm.belnauka.by/jour/article/download/601/498","source":{"id":"https://openalex.org/S4210199298","display_name":"Proceedings of the National Academy of Sciences of Belarus Physics and Mathematics Series","issn_l":"1561-2430","issn":["1561-2430","2524-2415"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["poland-20","russia-white-list-4"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://vestifm.belnauka.by/jour/article/download/601/498","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064252758","display_name":"Anton P. Ryabushko","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I45812101","display_name":"Belarusian National Technical University","ror":"https://ror.org/040a2r459","country_code":"BY","type":"education","lineage":["https://openalex.org/I45812101"]}],"countries":["BY"],"is_corresponding":false,"raw_author_name":"A. P. Ryabushko","raw_affiliation_strings":["Belarusian National Technical University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Belarusian National Technical University","institution_ids":["https://openalex.org/I45812101"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004201543","display_name":"\u0422\u0430\u0442\u044c\u044f\u043d\u0430 \u0410\u043d\u0442\u043e\u043d\u043e\u0432\u043d\u0430 \u0416\u0443\u0440","orcid":"https://orcid.org/0000-0003-4534-0298","observed_orcids":["https://orcid.org/0000-0003-4534-0298"]},"institutions":[{"id":"https://openalex.org/I4210094077","display_name":"Belarusian State Agrarian Technical University","ror":"https://ror.org/00n1ygd32","country_code":"BY","type":"education","lineage":["https://openalex.org/I4210094077"]}],"countries":["BY"],"is_corresponding":false,"raw_author_name":"T. A. Zhur","raw_affiliation_strings":["Belarusian State Agrarian Technical University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Belarusian State Agrarian Technical University","institution_ids":["https://openalex.org/I4210094077"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.38,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.53104089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"57","issue":"3","first_page":"330","last_page":"346"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.5327000021934509,"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":0.5327000021934509,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.4417000114917755,"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":0.003800000064074993,"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/lagrange-points","display_name":"Lagrange points","score":0.8650000095367432},{"id":"https://openalex.org/keywords/circular-restricted-three-body-problem","display_name":"circular restricted three-body problem","score":0.9369999766349792},{"id":"https://openalex.org/keywords/homogeneous-media","display_name":"homogeneous media","score":0.49000000953674316},{"id":"https://openalex.org/keywords/inhomogeneous-medium","display_name":"inhomogeneous medium","score":0.9919999837875366},{"id":"https://openalex.org/keywords/post-newtonian-expansion","display_name":"post-Newtonian approximation","score":0.8679999709129333},{"id":"https://openalex.org/keywords/general-relativity","display_name":"general relativity","score":0.8569999933242798},{"id":"https://openalex.org/keywords/relativistic-effects","display_name":"relativistic effects","score":0.4359999895095825},{"id":"https://openalex.org/keywords/solar-system-dynamics","display_name":"solar system dynamics","score":0.5540000200271606},{"id":"https://openalex.org/keywords/planetary-systems","display_name":"planetary systems","score":0.5180000066757202},{"id":"https://openalex.org/keywords/celestial-mechanics","display_name":"celestial mechanics","score":0.32199999690055847}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.695611298084259},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.6726495027542114},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.6622574329376221},{"id":"https://openalex.org/C140619461","wikidata":"https://www.wikidata.org/wiki/Q190463","display_name":"Lagrangian point","level":2,"score":0.5886337757110596},{"id":"https://openalex.org/C149324446","wikidata":"https://www.wikidata.org/wiki/Q43514","display_name":"Theory of relativity","level":2,"score":0.5762108564376831},{"id":"https://openalex.org/C294558","wikidata":"https://www.wikidata.org/wiki/Q366968","display_name":"Newtonian fluid","level":2,"score":0.5582411289215088},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.5109073519706726},{"id":"https://openalex.org/C98133451","wikidata":"https://www.wikidata.org/wiki/Q6542718","display_name":"Libration (molecule)","level":3,"score":0.4961148202419281},{"id":"https://openalex.org/C5594486","wikidata":"https://www.wikidata.org/wiki/Q161635","display_name":"Angular velocity","level":2,"score":0.455003023147583},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.41975271701812744},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2992195785045624},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20051240921020508},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1041097342967987}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.29235/1561-2430-2021-57-3-330-346","doi":"https://doi.org/10.29235/1561-2430-2021-57-3-330-346","is_oa":true,"landing_page_url":"https://doi.org/10.29235/1561-2430-2021-57-3-330-346","pdf_url":"https://vestifm.belnauka.by/jour/article/download/601/498","source":{"id":"https://openalex.org/S4210199298","display_name":"Proceedings of the National Academy of Sciences of Belarus Physics and Mathematics Series","issn_l":"1561-2430","issn":["1561-2430","2524-2415"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["poland-20","russia-white-list-4"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","raw_type":"journal-article"},{"id":"pmh:oai:oai.vestifm.elpub.ru:article/601","doi":null,"is_oa":true,"landing_page_url":"https://vestifm.belnauka.by/jour/article/view/601","pdf_url":null,"source":{"id":"https://openalex.org/S4306401792","display_name":"Izvestiya of the National Academy of Sciences of Belarus. Series of physical and mathematical sciences (Belarusian Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I151823869","host_organization_name":"National Academy of Sciences of Belarus","host_organization_lineage":["https://openalex.org/I151823869"],"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":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series; \u0422\u043e\u043c 57, \u2116 3 (2021); 330-346","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.29235/1561-2430-2021-57-3-330-346","doi":"https://doi.org/10.29235/1561-2430-2021-57-3-330-346","is_oa":true,"landing_page_url":"https://doi.org/10.29235/1561-2430-2021-57-3-330-346","pdf_url":"https://vestifm.belnauka.by/jour/article/download/601/498","source":{"id":"https://openalex.org/S4210199298","display_name":"Proceedings of the National Academy of Sciences of Belarus Physics and Mathematics Series","issn_l":"1561-2430","issn":["1561-2430","2524-2415"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["poland-20","russia-white-list-4"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3206234918.pdf","grobid_xml":"https://content.openalex.org/works/W3206234918.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W196733689","https://openalex.org/W1484586288","https://openalex.org/W2017378942","https://openalex.org/W2029677129","https://openalex.org/W2063010836","https://openalex.org/W2923202279","https://openalex.org/W3006225065","https://openalex.org/W3010223429","https://openalex.org/W3042971708","https://openalex.org/W3112371649","https://openalex.org/W3169087353","https://openalex.org/W4253415285"],"related_works":["https://openalex.org/W3006203111","https://openalex.org/W7098346778","https://openalex.org/W2183392013","https://openalex.org/W3040009068","https://openalex.org/W1965930868","https://openalex.org/W2018451375","https://openalex.org/W3197724494","https://openalex.org/W6991059987","https://openalex.org/W2561358802","https://openalex.org/W3161292770"],"abstract_inverted_index":{"Herein,":[0],"the":[1,28,34,51,54,66,70,77,82,90,92,95,104,110,114,127,131,147,176,180,186,190,195,208,212,225,231,237,248,257,261,269,277,294,301,305,313,319,322,325,333,337,348,353,363,369,377,383,405,408,421,433,436,451,456,461,464,471],"restricted":[2],"circular":[3],"three-body":[4],"problem":[5,462],"in":[6,27,65,89,109,155,203,207,256,276,293,300,357,362,382,432,468,470],"homogeneous":[7,100,205,298,358],"and":[8,30,45,133,351,359,365,380,385,390,430,442],"inhomogeneous":[9,241,360],"media":[10,361,469],"is":[11,15,315,445,476],"considered.":[12],"Particular":[13],"attention":[14],"paid":[16],"to":[17,50,185,318],"libration":[18,135,152,232,326],"points.":[19],"The":[20,222,310,424],"conditions":[21],"of":[22,33,37,53,60,63,69,72,81,84,103,113,117,151,179,183,189,193,197,199,211,215,224,239,250,252,260,264,296,304,308,321,339,368,372,376,407,410,416,420,427,435,438,450,463,466,474],"their":[23,164,443],"existence":[24,320],"or":[25],"non-existence":[26],"Newtonian":[29,44,111,177,209,258,364],"post-Newtonian":[31,187,302,366],"approximations":[32,367],"general":[35,115,181,191,213,262,306,370,472],"theory":[36,116,182,192,214,263,307,371,473],"relativity":[38,118,184,475],"are":[39,74,120,330,343,393],"derived.":[40],"Several":[41],"regularities,":[42],"new":[43],"relativistic":[46,56],"e\ufb00ects":[47,381,431],"arising":[48],"due":[49],"impact":[52],"additional":[55],"forces":[57],"on":[58,460],"bodies":[59,73,86,226,280,340,467],"gravitational":[61],"\ufb01elds":[62],"mediums":[64,392],"di\ufb00erential":[67],"equations":[68,80],"motion":[71,83,465],"indicated.":[75],"Using":[76],"previously":[78],"derived":[79],"two":[85,200,253],"A1,":[87,159,281,341],"A2":[88,160,282,342],"medium,":[91],"authors":[93],"substantiated":[94],"following":[96],"statements.":[97],"In":[98,236,332],"a":[99,156,204,220,290,297],"medium":[101,105,206,242,299],"(density":[102],"\u03c1":[106],"=":[107,346],"const)":[108],"approximation":[112,178,188,210,259,303],"there":[119],"\u03c1-libration":[121,354],"points":[122,136,153,233,355],",":[123,144],"1,...,5,":[124],"moving":[125],"along":[126,163,219,268],"same":[128],"circles":[129,165],"as":[130,292,404],"Euler":[132],"Lagrangian":[134],"Li":[137,154,234,328],"but":[138],"with":[139,166,400],"an":[140,167,240],"angular":[141,148,168],"velocity":[142,149,169],"0":[143,170],"greater":[145],"than":[146],"\u03c90":[150],"vacuum.":[157],"Bodies":[158],"also":[161],"move":[162,218,267],">":[171],"w":[172],"When":[173],"passing":[174],"from":[175],"relativity,":[194,216,265],"centre":[196,249,409],"mass":[198,251],"bodies,":[201,254],"resting":[202],"must":[217,266,283],"cycloid.":[221],"trajectories":[223],"can":[227,412],"not":[228],"be":[229],"circles,":[230],"disappear.":[235],"case":[238,295],"distributed,":[243],"for":[244],"example,":[245,397],"spherically":[246],"symmetrically,":[247],"already":[255],"cycloid,":[270],"despite":[271],"it":[272],"was":[273],"at":[274],"rest":[275],"void.":[278],"Therefore,":[279],"describe":[284],"loops":[285],"that":[286],"form,":[287],"\ufb01guratively":[288],"speaking,":[289],"\u00ablace\u00bb,":[291],"relativity.":[309,373],"\ufb01gure":[311],"illustrating":[312],"situation":[314],"provided.":[316],"Due":[317],"\u00ablace\u00bb":[323],"e\ufb00ect,":[324],"point":[327],"movements":[329],"destroyed.":[331],"special":[334],"case,":[335],"when":[336],"masses":[338],"equal":[344],"(m1":[345],"m2),":[347],"cycloids":[349],"disappear":[350],"all":[352],"exist":[356],"Numerical":[374],"estimates":[375],"predicted":[378],"patterns":[379],"Solar":[384],"other":[386],"planetary":[387,439],"systems,":[388,440],"interstellar":[389],"intergalactic":[391],"carried":[394,453],"out.":[395],"For":[396],"displacements":[398],"associated":[399],"these":[401,428],"e\ufb00ects,":[402],"such":[403],"displacement":[406],"mass,":[411],"reach":[413],"many":[414],"billions":[415],"kilometres":[417],"per":[418],"revolution":[419],"two-body":[422],"system.":[423],"possible":[425],"role":[426],"regularities":[429],"theories":[434],"evolution":[437],"galaxies,":[441],"ensembles":[444],"discussed.":[446],"A":[447],"brief":[448],"review":[449],"studies":[452],"out":[454],"by":[455],"Belarusian":[457],"scienti\ufb01c":[458],"school":[459],"given.":[477]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2021-10-25T00:00:00"}