{"id":"https://openalex.org/W4284891941","doi":"https://doi.org/10.3390/sym14071381","title":"Deployment and Retrieval Missions from Quasi-Periodic and Chaotic States under a Non-Linear Control Law","display_name":"Deployment and Retrieval Missions from Quasi-Periodic and Chaotic States under a Non-Linear Control Law","publication_year":2022,"publication_date":"2022-07-05","ids":{"openalex":"https://openalex.org/W4284891941","doi":"https://doi.org/10.3390/sym14071381"},"language":"en","primary_location":{"id":"doi:10.3390/sym14071381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071381","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1381/pdf?version=1657015762","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/7/1381/pdf?version=1657015762","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073855159","display_name":"Francisco Salazar","orcid":"https://orcid.org/0000-0002-3599-9745"},"institutions":[{"id":"https://openalex.org/I80849659","display_name":"Instituto Nacional de Pesquisas Espaciais","ror":"https://ror.org/04xbn6x09","country_code":"BR","type":"facility","lineage":["https://openalex.org/I4210151455","https://openalex.org/I80849659"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Francisco J. T. Salazar","raw_affiliation_strings":["National Institute for Space Research, Av. dos Astronautas-Campus do CTA, S\u00e3o Jos\u00e9 dos Campos 12227-010, SP, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-3599-9745","affiliations":[{"raw_affiliation_string":"National Institute for Space Research, Av. dos Astronautas-Campus do CTA, S\u00e3o Jos\u00e9 dos Campos 12227-010, SP, Brazil","institution_ids":["https://openalex.org/I80849659"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061035416","display_name":"A. F. B. A. Prado","orcid":"https://orcid.org/0000-0002-7966-3231"},"institutions":[{"id":"https://openalex.org/I126527374","display_name":"Peoples' Friendship University of Russia","ror":"https://ror.org/02dn9h927","country_code":"RU","type":"education","lineage":["https://openalex.org/I126527374"]},{"id":"https://openalex.org/I80849659","display_name":"Instituto Nacional de Pesquisas Espaciais","ror":"https://ror.org/04xbn6x09","country_code":"BR","type":"facility","lineage":["https://openalex.org/I4210151455","https://openalex.org/I80849659"]}],"countries":["BR","RU"],"is_corresponding":false,"raw_author_name":"Antonio B. A. Prado","raw_affiliation_strings":["Academy of Engineering, Peoples\u2019 Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia","National Institute for Space Research, Av. dos Astronautas-Campus do CTA, S\u00e3o Jos\u00e9 dos Campos 12227-010, SP, Brazil","Academy of Engineering, Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia"],"raw_orcid":"https://orcid.org/0000-0002-7966-3231","affiliations":[{"raw_affiliation_string":"Academy of Engineering, Peoples\u2019 Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]},{"raw_affiliation_string":"National Institute for Space Research, Av. dos Astronautas-Campus do CTA, S\u00e3o Jos\u00e9 dos Campos 12227-010, SP, Brazil","institution_ids":["https://openalex.org/I80849659"]},{"raw_affiliation_string":"Academy of Engineering, Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073855159"],"corresponding_institution_ids":["https://openalex.org/I80849659"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.1815,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.92926124,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"7","first_page":"1381","last_page":"1381"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11701","display_name":"Space Satellite Systems and Control","score":0.9994000196456909,"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/T11701","display_name":"Space Satellite Systems and Control","score":0.9994000196456909,"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":0.9984999895095825,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6397347450256348},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5659170746803284},{"id":"https://openalex.org/keywords/pendulum","display_name":"Pendulum","score":0.5453857183456421},{"id":"https://openalex.org/keywords/linear-motion","display_name":"Linear motion","score":0.45945650339126587},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.45824548602104187},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.45042407512664795},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.4226146936416626},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4046260118484497},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3751232624053955},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3568337559700012},{"id":"https://openalex.org/keywords/geodesy","display_name":"Geodesy","score":0.32681840658187866},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2718738913536072},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.2158539593219757},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.08244344592094421},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07585069537162781}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6397347450256348},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5659170746803284},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.5453857183456421},{"id":"https://openalex.org/C98068282","wikidata":"https://www.wikidata.org/wiki/Q2035846","display_name":"Linear motion","level":3,"score":0.45945650339126587},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.45824548602104187},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.45042407512664795},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.4226146936416626},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4046260118484497},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3751232624053955},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3568337559700012},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.32681840658187866},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2718738913536072},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.2158539593219757},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.08244344592094421},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07585069537162781},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym14071381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071381","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1381/pdf?version=1657015762","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e51db95777ea4f73a1ea31c160f0f0b5","is_oa":true,"landing_page_url":"https://doaj.org/article/e51db95777ea4f73a1ea31c160f0f0b5","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 7, p 1381 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/7/1381/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14071381","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry","raw_type":"Text"},{"id":"pmh:oai:urlib.net:sid.inpe.br/mtc-m21d/2022/07.20.13.06.21-0","is_oa":false,"landing_page_url":"http://urlib.net/sid.inpe.br/mtc-m21d/2022/07.20.13.06","pdf_url":null,"source":{"id":"https://openalex.org/S4377196298","display_name":"Biblioteca Digital da Mem\u00f3ria Cient\u00edfica do INPE (National Institute for Space Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I80849659","host_organization_name":"Instituto Nacional de Pesquisas Espaciais","host_organization_lineage":["https://openalex.org/I80849659"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"}],"best_oa_location":{"id":"doi:10.3390/sym14071381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071381","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1381/pdf?version=1657015762","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4284891941.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W104881878","https://openalex.org/W1570523361","https://openalex.org/W1672056153","https://openalex.org/W1837826213","https://openalex.org/W1964964021","https://openalex.org/W1971187928","https://openalex.org/W1971422912","https://openalex.org/W1972401022","https://openalex.org/W1979152159","https://openalex.org/W1979318336","https://openalex.org/W1980727363","https://openalex.org/W1981567398","https://openalex.org/W1984420709","https://openalex.org/W1988492771","https://openalex.org/W1989955124","https://openalex.org/W1993658356","https://openalex.org/W2012605933","https://openalex.org/W2013036394","https://openalex.org/W2027260178","https://openalex.org/W2038955274","https://openalex.org/W2061375081","https://openalex.org/W2065244343","https://openalex.org/W2076041763","https://openalex.org/W2080456847","https://openalex.org/W2082478233","https://openalex.org/W2090348288","https://openalex.org/W2096534027","https://openalex.org/W2100434057","https://openalex.org/W2125890673","https://openalex.org/W2322169914","https://openalex.org/W2326638946","https://openalex.org/W2330082391","https://openalex.org/W2489843674","https://openalex.org/W2523969417","https://openalex.org/W2735495089","https://openalex.org/W2806937467","https://openalex.org/W2942393480","https://openalex.org/W3047628880","https://openalex.org/W3184217010","https://openalex.org/W3213651135"],"related_works":["https://openalex.org/W2086182699","https://openalex.org/W2319641870","https://openalex.org/W2154449036","https://openalex.org/W4362664426","https://openalex.org/W228447877","https://openalex.org/W2375233219","https://openalex.org/W1982195085","https://openalex.org/W2632326683","https://openalex.org/W2104332279","https://openalex.org/W2721296288"],"abstract_inverted_index":{"When":[0],"the":[1,4,8,13,19,27,64,68,77,93,109,114,127,132,135,145,150,154,161],"length":[2],"of":[3,12,41,67,80,89,121,131],"tether":[5],"remains":[6],"constant,":[7],"relative":[9,65,128],"planar":[10],"motion":[11,60,66,112,130],"tethered":[14],"subsatellite":[15,69,133,151],"with":[16],"respect":[17],"to":[18,31,125,134,153],"base":[20],"satellite":[21],"in":[22],"a":[23,32,96,102],"circular":[24],"orbit":[25],"around":[26],"Earth,":[28],"is":[29,61,105,124],"similar":[30],"simple":[33],"pendulum":[34],"motion,":[35],"i.e.,":[36],"there":[37],"are":[38,51,85],"two":[39],"kinds":[40],"equilibrium":[42],"points:":[43],"local":[44,47,136,155],"vertical":[45,138,156],"and":[46,53,73,116,163],"horizontal":[48],"positions,":[49],"which":[50],"center":[52],"saddle":[54],"points,":[55],"respectively.":[56],"However,":[57],"when":[58],"out-of-plane":[59],"initially":[62],"excited,":[63],"presents":[70],"symmetric":[71],"quasi-periodic":[72,162],"chaotic":[74,164],"behavior.":[75],"In":[76,92],"first":[78],"part":[79],"this":[81,122],"study,":[82],"such":[83],"trajectories":[84],"analyzed":[86],"by":[87,100],"means":[88],"Poincar\u00e9":[90],"sections.":[91],"second":[94],"part,":[95],"non-linear":[97,129,146],"tension":[98,147],"force":[99],"using":[101],"Lyapunov":[103],"approach":[104],"proposed":[106],"for":[107],"controlling":[108],"coupled":[110],"pitch-roll":[111],"during":[113],"deployment":[115],"retrieval":[117],"phases.":[118],"The":[119,140],"goal":[120],"paper":[123],"guide":[126],"upward":[137],"position.":[139],"numerical":[141],"results":[142],"show":[143],"that":[144],"control":[148],"steered":[149],"close":[152],"direction":[157],"very":[158],"well,":[159],"reducing":[160],"oscillations.":[165]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}