{"id":"https://openalex.org/W4412003929","doi":"https://doi.org/10.3390/robotics14070094","title":"Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel Robots","display_name":"Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel Robots","publication_year":2025,"publication_date":"2025-07-03","ids":{"openalex":"https://openalex.org/W4412003929","doi":"https://doi.org/10.3390/robotics14070094"},"language":"en","primary_location":{"id":"doi:10.3390/robotics14070094","is_oa":true,"landing_page_url":"https://doi.org/10.3390/robotics14070094","pdf_url":"https://www.mdpi.com/2218-6581/14/7/94/pdf?version=1751612145","source":{"id":"https://openalex.org/S4210232487","display_name":"Robotics","issn_l":"2218-6581","issn":["2218-6581"],"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":"Robotics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2218-6581/14/7/94/pdf?version=1751612145","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001037606","display_name":"Francisco Cuenca Jim\u00e9nez","orcid":"https://orcid.org/0000-0002-8372-464X"},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Francisco Cuenca Jim\u00e9nez","raw_affiliation_strings":["Engineering Design Department, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad de M\u00e9xico 04510, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Engineering Design Department, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad de M\u00e9xico 04510, Mexico","institution_ids":["https://openalex.org/I8961855"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043939056","display_name":"Eusebio Jim\u00e9nez L\u00f3pez","orcid":"https://orcid.org/0000-0001-6893-3550"},"institutions":[{"id":"https://openalex.org/I4210120585","display_name":"Universidad Tecnol\u00f3gica del Sur de Sonora","ror":"https://ror.org/02f72qf66","country_code":"MX","type":"education","lineage":["https://openalex.org/I4210120585"]},{"id":"https://openalex.org/I4210149727","display_name":"Universidad La Salle","ror":"https://ror.org/05c99rg80","country_code":"MX","type":"education","lineage":["https://openalex.org/I4210149727"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Eusebio Jim\u00e9nez L\u00f3pez","raw_affiliation_strings":["Research and Development Department, Universidad Tecnol\u00f3gica del Sur de Sonora-Universidad La Salle Noroeste-ITESCA, Cuidad Obreg\u00f3n 85190, Sonora, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research and Development Department, Universidad Tecnol\u00f3gica del Sur de Sonora-Universidad La Salle Noroeste-ITESCA, Cuidad Obreg\u00f3n 85190, Sonora, Mexico","institution_ids":["https://openalex.org/I4210120585","https://openalex.org/I4210149727"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035639514","display_name":"Mario Acosta Flores","orcid":"https://orcid.org/0000-0003-3131-1509"},"institutions":[{"id":"https://openalex.org/I884181516","display_name":"Universidad Aut\u00f3noma del Estado de Morelos","ror":"https://ror.org/03rzb4f20","country_code":"MX","type":"education","lineage":["https://openalex.org/I884181516"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Mario Acosta Flores","raw_affiliation_strings":["Faculty of Chemical Sciences and Engineering, Universidad Aut\u00f3noma del Estado de Morelos, Cuernacava 62209, Morelos, Mexico"],"raw_orcid":"https://orcid.org/0000-0003-3131-1509","affiliations":[{"raw_affiliation_string":"Faculty of Chemical Sciences and Engineering, Universidad Aut\u00f3noma del Estado de Morelos, Cuernacava 62209, Morelos, Mexico","institution_ids":["https://openalex.org/I884181516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062025127","display_name":"F. Pe\u00f1u\u00f1uri","orcid":"https://orcid.org/0000-0003-1069-3499"},"institutions":[{"id":"https://openalex.org/I23878562","display_name":"Autonomous University of Yucat\u00e1n","ror":"https://ror.org/032p1n739","country_code":"MX","type":"education","lineage":["https://openalex.org/I23878562"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"F. Pe\u00f1u\u00f1uri","raw_affiliation_strings":["Faculty of Engineering, Universidad Aut\u00f3noma de Yucat\u00e1n, M\u00e9rida 97160, Yucat\u00e1n, Mexico"],"raw_orcid":"https://orcid.org/0000-0003-1069-3499","affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Universidad Aut\u00f3noma de Yucat\u00e1n, M\u00e9rida 97160, Yucat\u00e1n, Mexico","institution_ids":["https://openalex.org/I23878562"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064685462","display_name":"R. Pe\u00f3n-Escalante","orcid":"https://orcid.org/0000-0002-5361-7763"},"institutions":[{"id":"https://openalex.org/I23878562","display_name":"Autonomous University of Yucat\u00e1n","ror":"https://ror.org/032p1n739","country_code":"MX","type":"education","lineage":["https://openalex.org/I23878562"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Ricardo Javier Pe\u00f3n Escalante","raw_affiliation_strings":["Faculty of Engineering, Universidad Aut\u00f3noma de Yucat\u00e1n, M\u00e9rida 97160, Yucat\u00e1n, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-5361-7763","affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Universidad Aut\u00f3noma de Yucat\u00e1n, M\u00e9rida 97160, Yucat\u00e1n, Mexico","institution_ids":["https://openalex.org/I23878562"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039195787","display_name":"Juan Jos\u00e9 Delf\u00edn V\u00e1zquez","orcid":null},"institutions":[{"id":"https://openalex.org/I36020712","display_name":"Sonora Institute of Technology","ror":"https://ror.org/01v10fv91","country_code":"MX","type":"education","lineage":["https://openalex.org/I36020712"]},{"id":"https://openalex.org/I4210090124","display_name":"Tecnol\u00f3gico Nacional de M\u00e9xico","ror":"https://ror.org/00davry38","country_code":"MX","type":"government","lineage":["https://openalex.org/I1302736544","https://openalex.org/I4210090124","https://openalex.org/I4405258672"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Juan Jos\u00e9 Delf\u00edn V\u00e1zquez","raw_affiliation_strings":["Research and Development Department, Tecnol\u00f3gico Nacional de M\u00e9xico/ITS de Cajeme, Cuidad Obreg\u00f3n 85024, Sonora, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research and Development Department, Tecnol\u00f3gico Nacional de M\u00e9xico/ITS de Cajeme, Cuidad Obreg\u00f3n 85024, Sonora, Mexico","institution_ids":["https://openalex.org/I36020712","https://openalex.org/I4210090124"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5043939056"],"corresponding_institution_ids":["https://openalex.org/I4210120585","https://openalex.org/I4210149727"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.5174,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.61759105,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"14","issue":"7","first_page":"94","last_page":"94"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9904000163078308,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/quaternion","display_name":"Quaternion","score":0.8189822435379028},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.6981172561645508},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6659551858901978},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5687905550003052},{"id":"https://openalex.org/keywords/robotics","display_name":"Robotics","score":0.5393933653831482},{"id":"https://openalex.org/keywords/multibody-system","display_name":"Multibody system","score":0.4580897092819214},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.45229753851890564},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4178374111652374},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.39465540647506714},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.3822069764137268},{"id":"https://openalex.org/keywords/aerospace-engineering","display_name":"Aerospace engineering","score":0.35305148363113403},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.27474039793014526},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27458876371383667},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2730357348918915},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2451918125152588},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.14914408326148987},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14435863494873047},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.10127121210098267},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.08849340677261353}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.8189822435379028},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.6981172561645508},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6659551858901978},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5687905550003052},{"id":"https://openalex.org/C34413123","wikidata":"https://www.wikidata.org/wiki/Q170978","display_name":"Robotics","level":3,"score":0.5393933653831482},{"id":"https://openalex.org/C67865112","wikidata":"https://www.wikidata.org/wiki/Q1917564","display_name":"Multibody system","level":2,"score":0.4580897092819214},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.45229753851890564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4178374111652374},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.39465540647506714},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3822069764137268},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.35305148363113403},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.27474039793014526},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27458876371383667},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2730357348918915},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2451918125152588},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14914408326148987},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14435863494873047},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.10127121210098267},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.08849340677261353},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/robotics14070094","is_oa":true,"landing_page_url":"https://doi.org/10.3390/robotics14070094","pdf_url":"https://www.mdpi.com/2218-6581/14/7/94/pdf?version=1751612145","source":{"id":"https://openalex.org/S4210232487","display_name":"Robotics","issn_l":"2218-6581","issn":["2218-6581"],"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":"Robotics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:49ff8c6262bc486c806cfc21ad48a87e","is_oa":true,"landing_page_url":"https://doaj.org/article/49ff8c6262bc486c806cfc21ad48a87e","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":"Robotics, Vol 14, Iss 7, p 94 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/robotics14070094","is_oa":true,"landing_page_url":"https://doi.org/10.3390/robotics14070094","pdf_url":"https://www.mdpi.com/2218-6581/14/7/94/pdf?version=1751612145","source":{"id":"https://openalex.org/S4210232487","display_name":"Robotics","issn_l":"2218-6581","issn":["2218-6581"],"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":"Robotics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313925","display_name":"De La Salle University","ror":"https://ror.org/04xftk194"},{"id":"https://openalex.org/F4320323401","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25"},{"id":"https://openalex.org/F4320324462","display_name":"Universidad Aut\u00f3noma del Estado de Morelos","ror":"https://ror.org/03rzb4f20"},{"id":"https://openalex.org/F4320326060","display_name":"Universidad Aut\u00f3noma de Yucat\u00e1n","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412003929.pdf","grobid_xml":"https://content.openalex.org/works/W4412003929.grobid-xml"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W1504705348","https://openalex.org/W1560270123","https://openalex.org/W1798818154","https://openalex.org/W1969800098","https://openalex.org/W2005579615","https://openalex.org/W2027831574","https://openalex.org/W2084121184","https://openalex.org/W2132642682","https://openalex.org/W2487306105","https://openalex.org/W2586608414","https://openalex.org/W2607849048","https://openalex.org/W2610977893","https://openalex.org/W2722385933","https://openalex.org/W2727911935","https://openalex.org/W2785045183","https://openalex.org/W2789079847","https://openalex.org/W2795898617","https://openalex.org/W2810741444","https://openalex.org/W2811291653","https://openalex.org/W2888730209","https://openalex.org/W2896316488","https://openalex.org/W2903814689","https://openalex.org/W2906293295","https://openalex.org/W2954963222","https://openalex.org/W2964588158","https://openalex.org/W2965360662","https://openalex.org/W2973031530","https://openalex.org/W2984313780","https://openalex.org/W2999074679","https://openalex.org/W3007449369","https://openalex.org/W3013075150","https://openalex.org/W3018677067","https://openalex.org/W3038848529","https://openalex.org/W3041107080","https://openalex.org/W3042400005","https://openalex.org/W3085966781","https://openalex.org/W3096325641","https://openalex.org/W3114776659","https://openalex.org/W3119208799","https://openalex.org/W3156862228","https://openalex.org/W3163463203","https://openalex.org/W3165134901","https://openalex.org/W3165352287","https://openalex.org/W3197117360","https://openalex.org/W3214820869","https://openalex.org/W4200338325","https://openalex.org/W4200620562","https://openalex.org/W4220811523","https://openalex.org/W4223515733","https://openalex.org/W4224067835","https://openalex.org/W4283166196","https://openalex.org/W4387101020","https://openalex.org/W4387735432","https://openalex.org/W4390738627","https://openalex.org/W4393530134","https://openalex.org/W4403741229","https://openalex.org/W4407913994","https://openalex.org/W4409191308","https://openalex.org/W6653223607","https://openalex.org/W6661041901"],"related_works":["https://openalex.org/W3127350447","https://openalex.org/W3108700312","https://openalex.org/W4225472102","https://openalex.org/W2382948573","https://openalex.org/W2887325221","https://openalex.org/W2084651007","https://openalex.org/W2184550115","https://openalex.org/W3121191907","https://openalex.org/W2391028436","https://openalex.org/W4410606217"],"abstract_inverted_index":{"Quaternions":[0],"are":[1],"used":[2],"in":[3,7,20,24,28],"various":[4],"applications,":[5],"especially":[6],"those":[8],"where":[9],"it":[10],"is":[11,56],"necessary":[12],"to":[13,43],"model":[14,44,89],"and":[15,23,36,67,97,100,107,139,148,164,171],"represent":[16],"rotational":[17],"movements,":[18],"both":[19,83,117,162],"the":[21,29,32,45,74,111,123,134,149,155,159,165],"plane":[22],"space,":[25],"such":[26],"as":[27],"modeling":[30,146],"of":[31,34,48,53,93,103,113,119,122,129,151,158,161,167],"movements":[33,160],"robots":[35,60,163],"mechanisms.":[37],"In":[38],"this":[39],"article,":[40],"a":[41,63,68,91,101],"methodology":[42,147],"rigid":[46],"rotations":[47],"coupled":[49],"bodies":[50],"by":[51],"means":[52],"unit":[54],"quaternions":[55,153],"presented.":[57],"Two":[58],"parallel":[59],"were":[61,80,121,131],"modeled:":[62],"planar":[64,86],"RRR":[65,87],"robot":[66,72,88,115],"spatial":[69],"motion":[70],"PRRS":[71],"using":[73,133],"proposed":[75],"methodology.":[76],"Inverse":[77],"kinematic":[78],"problems":[79],"formulated":[81],"for":[82,110],"models.":[84],"The":[85,127,145],"generated":[90],"system":[92,102],"21":[94],"nonlinear":[95,105,136],"equations":[96,106,120,130],"18":[98],"unknowns":[99,109],"36":[104],"33":[108],"case":[112],"space":[114],"PRRS;":[116],"systems":[118,128],"polynomial":[124],"algebraic":[125],"type.":[126],"solved":[132],"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno":[135],"programming":[137],"algorithm":[138],"Mathematica":[140],"V12":[141],"symbolic":[142],"computation":[143],"software.":[144],"algebra":[150],"unitary":[152],"allowed":[154],"systematic":[156],"study":[157],"generation":[166],"mathematical":[168],"models":[169],"clearly":[170],"functionally.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}