{"id":"https://openalex.org/W2100020546","doi":"https://doi.org/10.1137/1037044","title":"Stabilization of the Inverted Linearized Pendulum by High Frequency Vibrations","display_name":"Stabilization of the Inverted Linearized Pendulum by High Frequency Vibrations","publication_year":1995,"publication_date":"1995-06-01","ids":{"openalex":"https://openalex.org/W2100020546","doi":"https://doi.org/10.1137/1037044","mag":"2100020546"},"language":"en","primary_location":{"id":"doi:10.1137/1037044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1037044","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5054211978","display_name":"Mark Levi","orcid":"https://orcid.org/0000-0001-6345-9079"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mark Levi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5050562889","display_name":"Warren Weckesser","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Warren Weckesser","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054211978"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0068,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.75915514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"37","issue":"2","first_page":"219","last_page":"223"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inverted-pendulum","display_name":"Inverted pendulum","score":0.7282872796058655},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.6539360284805298},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5359262824058533},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4394854009151459},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3493853211402893},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32849937677383423},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.32389721274375916},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.3221587538719177},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24649971723556519},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12281283736228943},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10591691732406616}],"concepts":[{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.7282872796058655},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.6539360284805298},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5359262824058533},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4394854009151459},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3493853211402893},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32849937677383423},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.32389721274375916},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.3221587538719177},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24649971723556519},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12281283736228943},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10591691732406616},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/1037044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1037044","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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":11,"referenced_works":["https://openalex.org/W564461737","https://openalex.org/W1547590019","https://openalex.org/W1586992199","https://openalex.org/W1989082180","https://openalex.org/W2093441125","https://openalex.org/W2094083160","https://openalex.org/W2123027230","https://openalex.org/W2151792940","https://openalex.org/W2491692976","https://openalex.org/W2742233052","https://openalex.org/W2971304175"],"related_works":["https://openalex.org/W962423920","https://openalex.org/W2387968248","https://openalex.org/W2350715914","https://openalex.org/W2120821724","https://openalex.org/W2379529020","https://openalex.org/W2101175215","https://openalex.org/W2893549521","https://openalex.org/W2330311678","https://openalex.org/W2352322616","https://openalex.org/W2574438335"],"abstract_inverted_index":{"In":[0],"this":[1],"note":[2],"we":[3],"give":[4],"a":[5],"simple":[6],"geometrical":[7],"picture":[8],"that":[9],"explains":[10],"why":[11],"an":[12],"inverted":[13],"pendulum":[14],"is":[15],"stabilized":[16],"by":[17],"high":[18],"frequency":[19],"vibrations.MSC":[20],"codes34A2634D1070J25Keywordsstabilityhyperbolic":[21],"and":[22],"elliptic":[23],"rotationsapplications":[24],"of":[25],"linear":[26],"algebra":[27]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}