{"id":"https://openalex.org/W4309864805","doi":"https://doi.org/10.1109/tcsi.2022.3223726","title":"The Frenet Frame as a Generalization of the Park Transform","display_name":"The Frenet Frame as a Generalization of the Park Transform","publication_year":2022,"publication_date":"2022-11-24","ids":{"openalex":"https://openalex.org/W4309864805","doi":"https://doi.org/10.1109/tcsi.2022.3223726"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2022.3223726","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2022.3223726","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","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/A5055696539","display_name":"Federico Milano","orcid":"https://orcid.org/0000-0002-0049-9185"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"Federico Milano","raw_affiliation_strings":["School of Electrical and Electronic Engineering, University College Dublin, Belfield, Dublin 4, Ireland"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, University College Dublin, Belfield, Dublin 4, Ireland","institution_ids":["https://openalex.org/I100930933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055696539"],"corresponding_institution_ids":["https://openalex.org/I100930933"],"apc_list":null,"apc_paid":null,"fwci":1.2153,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.78404423,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"70","issue":"2","first_page":"966","last_page":"976"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9588000178337097,"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9588000178337097,"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/T10805","display_name":"Vehicle Dynamics and Control Systems","score":0.9581999778747559,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/T13644","display_name":"Control Systems in Engineering","score":0.9567999839782715,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/frenet\u2013serret-formulas","display_name":"Frenet\u2013Serret formulas","score":0.9890170097351074},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6572022438049316},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.5793206691741943},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5766928195953369},{"id":"https://openalex.org/keywords/reference-frame","display_name":"Reference frame","score":0.5121819972991943},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.46919628977775574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3930942118167877},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.253142386674881},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25247693061828613},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.1191135048866272}],"concepts":[{"id":"https://openalex.org/C162546045","wikidata":"https://www.wikidata.org/wiki/Q947922","display_name":"Frenet\u2013Serret formulas","level":3,"score":0.9890170097351074},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6572022438049316},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.5793206691741943},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5766928195953369},{"id":"https://openalex.org/C172849965","wikidata":"https://www.wikidata.org/wiki/Q3148875","display_name":"Reference frame","level":3,"score":0.5121819972991943},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.46919628977775574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3930942118167877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.253142386674881},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25247693061828613},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.1191135048866272},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2022.3223726","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2022.3223726","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7400000095367432,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G5110325343","display_name":null,"funder_award_id":"RDD/00681","funder_id":"https://openalex.org/F4320320848","funder_display_name":"Sustainable Energy Authority of Ireland"},{"id":"https://openalex.org/G7961056894","display_name":null,"funder_award_id":"883710","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320848","display_name":"Sustainable Energy Authority of Ireland","ror":"https://ror.org/015j3sb07"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1504985399","https://openalex.org/W1517452805","https://openalex.org/W1548863556","https://openalex.org/W1790588527","https://openalex.org/W1978877729","https://openalex.org/W1984136257","https://openalex.org/W1984335232","https://openalex.org/W1988867235","https://openalex.org/W2016618808","https://openalex.org/W2073998266","https://openalex.org/W2100479030","https://openalex.org/W2107338474","https://openalex.org/W2111645751","https://openalex.org/W2149783401","https://openalex.org/W2154085245","https://openalex.org/W2171932063","https://openalex.org/W2265248459","https://openalex.org/W2483136505","https://openalex.org/W2490744814","https://openalex.org/W2808039293","https://openalex.org/W3040311900","https://openalex.org/W3048465714","https://openalex.org/W3166076697","https://openalex.org/W3197139174","https://openalex.org/W4205619206","https://openalex.org/W4206331147","https://openalex.org/W4206758614","https://openalex.org/W4236484401","https://openalex.org/W4246404318","https://openalex.org/W4298363721"],"related_works":["https://openalex.org/W2609788161","https://openalex.org/W2890994448","https://openalex.org/W4312766700","https://openalex.org/W1967787111","https://openalex.org/W2998181671","https://openalex.org/W2361423042","https://openalex.org/W4312095783","https://openalex.org/W156735263","https://openalex.org/W4299719436","https://openalex.org/W2952094119"],"abstract_inverted_index":{"The":[0,28,68,99],"paper":[1],"proposes":[2],"a":[3,16,108,113],"generalization":[4],"of":[5,19,48,52,70,101,110],"the":[6,11,41,46,49,53,59,63,88,102,118],"Park":[7],"transform":[8,31,55],"based":[9,76,116],"on":[10,77,117],"Frenet":[12,103],"frame,":[13],"which":[14,38],"is":[15,32,56,97],"special":[17],"set":[18],"coordinates":[20],"defined":[21],"in":[22],"differential":[23],"geometry":[24],"for":[25,35],"space":[26],"curves.":[27],"proposed":[29,54],"geometric":[30],"first":[33],"discussed":[34,57],"three":[36,95],"dimensions,":[37],"correspond":[39],"to":[40,90],"common":[42],"three-phase":[43],"circuits.":[44],"Then,":[45],"expression":[47],"time":[50],"derivative":[51],"and":[58,62,73,81],"Frenet-Serret":[60],"formulas":[61],"Darboux":[64],"vector":[65],"are":[66,84,105],"introduced.":[67],"change":[69],"reference":[71],"frame":[72,104],"its":[74],"differentiation":[75],"Cartan\u2019s":[78],"moving":[79],"frames":[80],"attitude":[82],"matrices":[83],"also":[85],"described.":[86],"Finally,":[87],"extension":[89],"circuits":[91],"with":[92],"more":[93],"than":[94],"phases":[96],"presented.":[98],"features":[100],"illustrated":[106],"through":[107],"variety":[109],"examples,":[111],"including":[112],"case":[114],"study":[115],"IEEE":[119],"39-bus":[120],"system.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2025-10-10T00:00:00"}