{"id":"https://openalex.org/W2074257552","doi":"https://doi.org/10.1137/s0363012999364176","title":"Averaging and Vibrational Control of Mechanical Systems","display_name":"Averaging and Vibrational Control of Mechanical Systems","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2074257552","doi":"https://doi.org/10.1137/s0363012999364176","mag":"2074257552"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012999364176","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012999364176","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5068353454","display_name":"Francesco Bullo","orcid":"https://orcid.org/0000-0002-4785-2118"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Francesco Bullo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5068353454"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":31.1412,"has_fulltext":false,"cited_by_count":190,"citation_normalized_percentile":{"value":0.99693002,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"41","issue":"2","first_page":"542","last_page":"562"},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9987999796867371,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9973999857902527,"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":0.8117989301681519},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.7442693710327148},{"id":"https://openalex.org/keywords/mechanical-system","display_name":"Mechanical system","score":0.6466726660728455},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6196086406707764},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.6127229332923889},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6073377132415771},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5571211576461792},{"id":"https://openalex.org/keywords/affine-connection","display_name":"Affine connection","score":0.4521137475967407},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.44594326615333557},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40839889645576477},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33037227392196655},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.20728713274002075},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.17941638827323914},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.11375349760055542},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0909779965877533}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8117989301681519},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.7442693710327148},{"id":"https://openalex.org/C171912257","wikidata":"https://www.wikidata.org/wiki/Q11019","display_name":"Mechanical system","level":2,"score":0.6466726660728455},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6196086406707764},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.6127229332923889},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6073377132415771},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5571211576461792},{"id":"https://openalex.org/C105561566","wikidata":"https://www.wikidata.org/wiki/Q1371213","display_name":"Affine connection","level":3,"score":0.4521137475967407},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.44594326615333557},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40839889645576477},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33037227392196655},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.20728713274002075},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.17941638827323914},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.11375349760055542},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0909779965877533},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0363012999364176","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012999364176","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5600000023841858,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1524590822","https://openalex.org/W1564897360","https://openalex.org/W1603340857","https://openalex.org/W1964373008","https://openalex.org/W1970464464","https://openalex.org/W1976166855","https://openalex.org/W1980330256","https://openalex.org/W1982404224","https://openalex.org/W1983118300","https://openalex.org/W1983885293","https://openalex.org/W2019575952","https://openalex.org/W2030394252","https://openalex.org/W2035660516","https://openalex.org/W2046988039","https://openalex.org/W2048603489","https://openalex.org/W2058113136","https://openalex.org/W2064854048","https://openalex.org/W2071355416","https://openalex.org/W2078282106","https://openalex.org/W2095925063","https://openalex.org/W2106781406","https://openalex.org/W2120851686","https://openalex.org/W2132336574","https://openalex.org/W2138642494","https://openalex.org/W2143810732","https://openalex.org/W2144026911","https://openalex.org/W2146826877","https://openalex.org/W2162931168","https://openalex.org/W2169121722","https://openalex.org/W2174733634","https://openalex.org/W2912522929","https://openalex.org/W3041070869","https://openalex.org/W3210839039","https://openalex.org/W4205424143","https://openalex.org/W4206033904","https://openalex.org/W4214690803","https://openalex.org/W4239216443","https://openalex.org/W4292872153"],"related_works":["https://openalex.org/W1965043874","https://openalex.org/W1577606234","https://openalex.org/W88265998","https://openalex.org/W1916844891","https://openalex.org/W25827740","https://openalex.org/W25683132","https://openalex.org/W1992045028","https://openalex.org/W1634204107","https://openalex.org/W44123443","https://openalex.org/W2120604406"],"abstract_inverted_index":{"This":[0,112],"paper":[1],"investigates":[2],"averaging":[3,18],"theory":[4,21,49],"and":[5,19,32,37,123,147,159],"oscillatory":[6],"control":[7,133],"for":[8,142],"a":[9,43,137],"large":[10],"class":[11],"of":[12,29,50,60,95,110,119,132,139,155],"mechanical":[13,61,143],"systems.":[14],"A":[15],"link":[16],"between":[17],"controllability":[20],"is":[22,73,91,105,126,145],"presented":[23,41],"by":[24,64],"relating":[25],"the":[26,48,58,88,93,108,117,129,153],"key":[27],"concepts":[28],"averaged":[30,71,120],"potential":[31,103,121],"symmetric":[33,130],"product.":[34],"Both":[35],"analysis":[36,54],"synthesis":[38],"results":[39],"are":[40,150],"within":[42],"coordinate-free":[44],"framework":[45],"based":[46],"on":[47,56],"affine":[51,78],"connections.":[52],"The":[53,70],"focuses":[55],"characterizing":[57],"behavior":[59],"systems":[62,96,144],"forced":[63],"high":[65,67],"amplitude":[66],"frequency":[68],"inputs.":[69],"system":[72,80],"shown":[74],"to":[75,82,100,128],"be":[76],"an":[77,83],"connection":[79],"subject":[81],"appropriate":[84],"forcing":[85],"term.":[86],"If":[87],"input":[89],"codistribution":[90],"integrable,":[92],"subclass":[94],"with":[97],"Hamiltonian":[98],"equal":[99],"\"kinetic":[101],"plus":[102],"energy\"":[104],"closed":[106],"under":[107],"operation":[109],"averaging.":[111],"result":[113],"precisely":[114],"characterizes":[115],"when":[116],"notion":[118,138],"arises":[122],"how":[124],"it":[125],"related":[127],"product":[131],"vector":[134],"fields.":[135],"Finally,":[136],"vibrational":[140],"stabilization":[141],"introduced,":[146],"sufficient":[148],"conditions":[149],"provided":[151],"in":[152],"form":[154],"linear":[156],"matrix":[157],"equality":[158],"inequality":[160],"tests.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":4}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}