{"id":"https://openalex.org/W1972150613","doi":"https://doi.org/10.1109/tro.2012.2193230","title":"Lagrangian Modeling of the Magnetization and the Magnetic Torque on Assembled Soft-Magnetic MEMS Devices for Fast Computation and Analysis","display_name":"Lagrangian Modeling of the Magnetization and the Magnetic Torque on Assembled Soft-Magnetic MEMS Devices for Fast Computation and Analysis","publication_year":2012,"publication_date":"2012-04-27","ids":{"openalex":"https://openalex.org/W1972150613","doi":"https://doi.org/10.1109/tro.2012.2193230","mag":"1972150613"},"language":"en","primary_location":{"id":"doi:10.1109/tro.2012.2193230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tro.2012.2193230","pdf_url":null,"source":{"id":"https://openalex.org/S144620930","display_name":"IEEE Transactions on Robotics","issn_l":"1552-3098","issn":["1552-3098","1546-1904","1941-0468"],"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 Robotics","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":null,"display_name":"Zolt\u00e1n Nagy","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Zolt\u00e1n Nagy","raw_affiliation_strings":["Department of Mechanical and Process Engineering, Institute of Robotics and Intelligent Systems, ETH Zurich, Zurich, Switzerland","Dept. of Mech. & Process Eng, ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Process Engineering, Institute of Robotics and Intelligent Systems, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Dept. of Mech. & Process Eng, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006427311","display_name":"Bradley J. Nelson","orcid":"https://orcid.org/0000-0001-9070-6987"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Bradley J. Nelson","raw_affiliation_strings":["Department of Mechanical and Process Engineering, Institute of Robotics and Intelligent Systems, ETH Zurich, Zurich, Switzerland","Dept. of Mech. & Process Eng, ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Process Engineering, Institute of Robotics and Intelligent Systems, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Dept. of Mech. & Process Eng, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.811,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.71428571,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"28","issue":"4","first_page":"787","last_page":"797"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11486","display_name":"Micro and Nano Robotics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11486","display_name":"Micro and Nano Robotics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T12784","display_name":"Modular Robots and Swarm Intelligence","score":0.9980000257492065,"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"}},{"id":"https://openalex.org/T11737","display_name":"Advanced Materials and Mechanics","score":0.996399998664856,"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/torque","display_name":"Torque","score":0.6503243446350098},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.6398969292640686},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.604797899723053},{"id":"https://openalex.org/keywords/magnetization","display_name":"Magnetization","score":0.5949891209602356},{"id":"https://openalex.org/keywords/saturation","display_name":"Saturation (graph theory)","score":0.5666242241859436},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5235280990600586},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5091373324394226},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.5050249695777893},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4328538477420807},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.41576218605041504},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.34641456604003906},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33138954639434814},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2755175232887268},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21425440907478333},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1775113046169281},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07539692521095276}],"concepts":[{"id":"https://openalex.org/C144171764","wikidata":"https://www.wikidata.org/wiki/Q48103","display_name":"Torque","level":2,"score":0.6503243446350098},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.6398969292640686},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.604797899723053},{"id":"https://openalex.org/C32546565","wikidata":"https://www.wikidata.org/wiki/Q856711","display_name":"Magnetization","level":3,"score":0.5949891209602356},{"id":"https://openalex.org/C9930424","wikidata":"https://www.wikidata.org/wiki/Q7426587","display_name":"Saturation (graph theory)","level":2,"score":0.5666242241859436},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5235280990600586},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5091373324394226},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.5050249695777893},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4328538477420807},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.41576218605041504},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.34641456604003906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33138954639434814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2755175232887268},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21425440907478333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1775113046169281},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07539692521095276},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tro.2012.2193230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tro.2012.2193230","pdf_url":null,"source":{"id":"https://openalex.org/S144620930","display_name":"IEEE Transactions on Robotics","issn_l":"1552-3098","issn":["1552-3098","1546-1904","1941-0468"],"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 Robotics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321652","display_name":"Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich","ror":"https://ror.org/05a28rw58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1978158070","https://openalex.org/W1982549141","https://openalex.org/W1990416424","https://openalex.org/W1992936359","https://openalex.org/W1994710268","https://openalex.org/W1995580444","https://openalex.org/W2020077517","https://openalex.org/W2037424018","https://openalex.org/W2049220874","https://openalex.org/W2094904022","https://openalex.org/W2095968026","https://openalex.org/W2101697338","https://openalex.org/W2104346436","https://openalex.org/W2116813238","https://openalex.org/W2144925909","https://openalex.org/W2157760711","https://openalex.org/W2161381314","https://openalex.org/W2163252428","https://openalex.org/W2168046319","https://openalex.org/W2169128775","https://openalex.org/W2989910212","https://openalex.org/W4230748214","https://openalex.org/W4235279454","https://openalex.org/W4250589301","https://openalex.org/W4302348355","https://openalex.org/W6769632136"],"related_works":["https://openalex.org/W2378760347","https://openalex.org/W2099351328","https://openalex.org/W3160132513","https://openalex.org/W2081441772","https://openalex.org/W2470048734","https://openalex.org/W4362524263","https://openalex.org/W4379538379","https://openalex.org/W1485761249","https://openalex.org/W2969769538","https://openalex.org/W4309207534"],"abstract_inverted_index":{"We":[0],"apply":[1],"the":[2,9,12,23,27,34,42,46,49,55,60,63,67,70,77,82,92,104,110],"Lagrangian":[3],"technique":[4],"to":[5,90,102],"compute":[6],"and":[7,11,37,48,79,120],"analyze":[8],"magnetization":[10,43],"magnetic":[13,71],"torque":[14,72,105],"on":[15,106],"soft-magnetic":[16],"shape-dominant":[17],"structures.":[18],"The":[19,52,114],"main":[20],"advantages":[21],"are":[22,116],"considerable":[24],"reduction":[25],"of":[26,41,54,66,69,76,81,95],"computation":[28,31],"time,":[29,62],"constant":[30],"times":[32],"across":[33],"saturation":[35,50,93],"limits,":[36],"a":[38,74,96],"closed-form":[39],"description":[40],"in":[44],"both":[45],"linear":[47],"region.":[51],"analysis":[53],"Lagrange":[56],"multiplier":[57],"allows,":[58],"for":[59],"first":[61],"analytic":[64],"prediction":[65],"evolution":[68],"as":[73],"function":[75],"direction":[78],"magnitude":[80],"applied":[83],"field.":[84],"In":[85],"addition,":[86],"it":[87],"allows":[88],"one":[89],"quantify":[91],"state":[94],"body,":[97],"which":[98],"is":[99],"then":[100],"used":[101],"predict":[103],"assembled":[107],"structures":[108],"where":[109],"classic":[111],"method":[112],"fails.":[113],"results":[115],"verified":[117],"by":[118],"experiments":[119],"finite":[121],"element":[122],"analysis.":[123]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}