{"id":"https://openalex.org/W2343074001","doi":"https://doi.org/10.1109/tac.2015.2463632","title":"Non-Minimal Order Model of Mechanical Systems With Redundant Constraints for Simulations and Controls","display_name":"Non-Minimal Order Model of Mechanical Systems With Redundant Constraints for Simulations and Controls","publication_year":2015,"publication_date":"2015-08-03","ids":{"openalex":"https://openalex.org/W2343074001","doi":"https://doi.org/10.1109/tac.2015.2463632","mag":"2343074001"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2015.2463632","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2463632","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/A5000948875","display_name":"Farhad Aghili","orcid":"https://orcid.org/0000-0002-2059-0226"},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]},{"id":"https://openalex.org/I2800055578","display_name":"Canadian Space Agency","ror":"https://ror.org/03a1gte98","country_code":"CA","type":"government","lineage":["https://openalex.org/I2800055578"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Farhad Aghili","raw_affiliation_strings":["Canadian Space Agency (CSA), Concordia University, Montreal, Canada"],"affiliations":[{"raw_affiliation_string":"Canadian Space Agency (CSA), Concordia University, Montreal, Canada","institution_ids":["https://openalex.org/I2800055578","https://openalex.org/I60158472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000948875"],"corresponding_institution_ids":["https://openalex.org/I2800055578","https://openalex.org/I60158472"],"apc_list":null,"apc_paid":null,"fwci":1.3464,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.84346546,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"61","issue":"5","first_page":"1350","last_page":"1355"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":1.0,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":1.0,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.996399998664856,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9961000084877014,"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/mass-matrix","display_name":"Mass matrix","score":0.6363294720649719},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5604739785194397},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5338678359985352},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5252568125724792},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5209592580795288},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5192463397979736},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5170291066169739},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4781454801559448},{"id":"https://openalex.org/keywords/oblique-projection","display_name":"Oblique projection","score":0.46093881130218506},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.45444828271865845},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44420310854911804},{"id":"https://openalex.org/keywords/generalized-coordinates","display_name":"Generalized coordinates","score":0.4268896281719208},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41507112979888916},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35957539081573486},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27375638484954834},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21430543065071106},{"id":"https://openalex.org/keywords/orthographic-projection","display_name":"Orthographic projection","score":0.20018744468688965},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1738845407962799},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15204480290412903}],"concepts":[{"id":"https://openalex.org/C135585149","wikidata":"https://www.wikidata.org/wiki/Q339704","display_name":"Mass matrix","level":3,"score":0.6363294720649719},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5604739785194397},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5338678359985352},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5252568125724792},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5209592580795288},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5192463397979736},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5170291066169739},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4781454801559448},{"id":"https://openalex.org/C161666082","wikidata":"https://www.wikidata.org/wiki/Q14551923","display_name":"Oblique projection","level":3,"score":0.46093881130218506},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.45444828271865845},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44420310854911804},{"id":"https://openalex.org/C105815890","wikidata":"https://www.wikidata.org/wiki/Q1057607","display_name":"Generalized coordinates","level":2,"score":0.4268896281719208},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41507112979888916},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35957539081573486},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27375638484954834},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21430543065071106},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.20018744468688965},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1738845407962799},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15204480290412903},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C185544564","wikidata":"https://www.wikidata.org/wiki/Q81197","display_name":"Nuclear physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2015.2463632","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2463632","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W41341799","https://openalex.org/W183122886","https://openalex.org/W1514056936","https://openalex.org/W1548645842","https://openalex.org/W1975722775","https://openalex.org/W2012990101","https://openalex.org/W2056690941","https://openalex.org/W2081415325","https://openalex.org/W2087051862","https://openalex.org/W2103561888","https://openalex.org/W2136096001","https://openalex.org/W2152737511","https://openalex.org/W2162495121","https://openalex.org/W6675946378"],"related_works":["https://openalex.org/W2154039962","https://openalex.org/W2131680091","https://openalex.org/W1988099423","https://openalex.org/W2033504252","https://openalex.org/W2081829404","https://openalex.org/W2618464896","https://openalex.org/W2016834887","https://openalex.org/W4300579289","https://openalex.org/W4299141160","https://openalex.org/W2088255893"],"abstract_inverted_index":{"This":[0],"technical":[1],"note":[2],"presents":[3],"a":[4,99],"non-minimal":[5],"order":[6],"dynamics":[7,41],"model":[8,39,137],"for":[9,124],"many":[10],"analysis,":[11],"simulation,":[12],"and":[13,129],"control":[14,140],"problems":[15],"of":[16,30,37,42,77,87,98,119,126,141,153],"constrained":[17,154],"mechanical":[18],"systems":[19],"passing":[20],"through":[21],"singular":[22,58],"configurations":[23],"during":[24],"their":[25],"motion":[26],"by":[27,117],"making":[28],"use":[29],"linear":[31],"projection":[32,122],"operator.":[33],"The":[34,48],"distinct":[35],"features":[36],"this":[38],"describing":[40],"the":[43,84,88,107],"dependent":[44,142,147],"coordinates":[45,143],"are:":[46],"(i)":[47],"mass":[49,90],"matrix":[50,61,91],"M\u0305(q)":[51],"is":[52,63,133],"always":[53],"positive":[54],"definite":[55],"even":[56],"at":[57],"configurations;":[59],"(ii)":[60],"M\u0305-2C\u0305":[62],"skew":[64],"symmetric,":[65],"where":[66],"all":[67],"nonlinear":[68],"terms":[69],"are":[70],"lumped":[71],"into":[72],"vector":[73],"C\u0305(q,q\u0307)q\u0307":[74],"after":[75],"elimination":[76],"constraint":[78,89,127],"forces.":[79,131],"Eigenvalue":[80],"analysis":[81],"shows":[82],"that":[83,135],"condition":[85],"number":[86],"can":[92],"be":[93],"minimized":[94],"upon":[95],"adequate":[96],"selection":[97],"scalar":[100],"parameter":[101],"called":[102],"\u201cvirtual":[103],"mass\u201d":[104],"thereby":[105],"reducing":[106],"sensitivity":[108],"to":[109],"round-off":[110],"errors":[111],"in":[112],"numerical":[113],"computation.":[114],"It":[115,132],"follows":[116],"derivation":[118],"two":[120],"oblique":[121],"matrices":[123],"computation":[125],"forces":[128],"actuation":[130],"shown":[134],"projection-based":[136],"allows":[138],"feedback":[139],"which,":[144],"unlike":[145],"reduced-order":[146],"coordinates,":[148],"uniquely":[149],"define":[150],"spatial":[151],"configuration":[152],"systems.":[155]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"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"}
