{"id":"https://openalex.org/W2000777285","doi":"https://doi.org/10.1109/tac.2012.2218671","title":"Geometric Criteria for the Quasi-Linearization of the Equations of Motion of Mechanical Systems","display_name":"Geometric Criteria for the Quasi-Linearization of the Equations of Motion of Mechanical Systems","publication_year":2012,"publication_date":"2012-09-14","ids":{"openalex":"https://openalex.org/W2000777285","doi":"https://doi.org/10.1109/tac.2012.2218671","mag":"2000777285"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2012.2218671","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2218671","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","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/A5090203902","display_name":"Dong Eui Chang","orcid":"https://orcid.org/0000-0002-6496-4189"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Dong Eui Chang","raw_affiliation_strings":["Department of Applied Mathematics, University of Waterloo, Waterloo, ONT, Canada","[Dept. of Applied Math., University of Waterloo, Waterloo, ON, Canada]"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Waterloo, Waterloo, ONT, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"[Dept. of Applied Math., University of Waterloo, Waterloo, ON, Canada]","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049430596","display_name":"R. G. McLenaghan","orcid":"https://orcid.org/0000-0002-8121-403X"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Raymond G. McLenaghan","raw_affiliation_strings":["Department of Applied Mathematics, University of Waterloo, Waterloo, ONT, Canada","[Dept. of Applied Math., University of Waterloo, Waterloo, ON, Canada]"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Waterloo, Waterloo, ONT, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"[Dept. of Applied Math., University of Waterloo, Waterloo, ON, Canada]","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090203902"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":3.3782,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.921196,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"4","first_page":"1046","last_page":"1050"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9993000030517578,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9993000030517578,"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":0.9929999709129333,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9689000248908997,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.743406355381012},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.6230295300483704},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6166908144950867},{"id":"https://openalex.org/keywords/tangent-bundle","display_name":"Tangent bundle","score":0.5292080044746399},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.5205377340316772},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.49840641021728516},{"id":"https://openalex.org/keywords/constant-curvature","display_name":"Constant curvature","score":0.4854341149330139},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.4725268483161926},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.44736576080322266},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.44166478514671326},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.4172886610031128},{"id":"https://openalex.org/keywords/fundamental-theorem-of-riemannian-geometry","display_name":"Fundamental theorem of Riemannian geometry","score":0.41689541935920715},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.339383602142334},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.31783825159072876},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.21861106157302856},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1713871955871582},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12832796573638916}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.743406355381012},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.6230295300483704},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6166908144950867},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.5292080044746399},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5205377340316772},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.49840641021728516},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.4854341149330139},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.4725268483161926},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.44736576080322266},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.44166478514671326},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.4172886610031128},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.41689541935920715},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.339383602142334},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.31783825159072876},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.21861106157302856},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1713871955871582},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12832796573638916},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2012.2218671","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2218671","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1485513406","https://openalex.org/W1495727713","https://openalex.org/W1514845098","https://openalex.org/W1571212840","https://openalex.org/W1855982673","https://openalex.org/W1983894121","https://openalex.org/W1989990825","https://openalex.org/W2026892575","https://openalex.org/W2102263452","https://openalex.org/W2107769032","https://openalex.org/W2155273341","https://openalex.org/W2160699865"],"related_works":["https://openalex.org/W1976330683","https://openalex.org/W2050728860","https://openalex.org/W3103229299","https://openalex.org/W3215620951","https://openalex.org/W2952578374","https://openalex.org/W1535135171","https://openalex.org/W1548805817","https://openalex.org/W133058030","https://openalex.org/W2100949341","https://openalex.org/W2000854007"],"abstract_inverted_index":{"A":[0,95],"linear":[1],"transformation":[2],"of":[3,15,17,40,67,91],"velocity":[4],"for":[5,98,118],"a":[6,41,113],"mechanical":[7,42,93],"system":[8,19,43],"is":[9,30,58,71,101,124,129],"said":[10],"to":[11,60,74,78],"quasi-linearize":[12],"the":[13,18,27,38,55,61,64,75,79,83,88,92,103,126,135,151,156],"equations":[14],"motion":[16],"if":[20],"it":[21],"eliminates":[22],"all":[23],"terms":[24],"quadratic":[25],"in":[26,45,148],"velocity.":[28],"It":[29],"well-known":[31],"that":[32,54,63,102,112,125,140],"controller/observer":[33],"synthesis":[34],"becomes":[35],"tractable":[36],"when":[37],"dynamics":[39],"are":[44],"quasi-linearized":[46],"form.":[47],"In":[48],"this":[49,99],"technical":[50],"note,":[51],"we":[52],"show":[53,111],"quasi-linearization":[56],"property":[57,62,100],"equivalent":[59],"Lie":[65],"algebra":[66],"Killing":[68],"vector":[69],"fields":[70],"pointwise":[72],"equal":[73],"tangent":[76],"space":[77],"configuration":[80],"manifold":[81,105],"with":[82],"Riemannian":[84,104,122,137],"metric":[85],"induced":[86],"by":[87],"mass":[89],"tensor":[90],"system.":[94],"sufficient":[96,116],"condition":[97,117,139,154,160],"be":[106,162],"locally":[107],"symmetric.":[108],"We":[109],"further":[110],"necessary":[114],"and":[115,155],"quasi-linearizability":[119],"on":[120],"2-D":[121],"manifolds":[123],"scalar":[127,158],"curvature":[128,138,159],"constant.":[130],"The":[131],"above":[132],"results":[133],"extend":[134],"zero":[136],"has":[141],"been":[142],"extensively":[143],"applied":[144],"since":[145],"its":[146],"introduction":[147],"1992.":[149],"Moreover,":[150],"local":[152],"symmetricity":[153],"constant":[157],"can":[161],"easily":[163],"verified":[164],"using":[165],"differentiation.":[166]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}