{"id":"https://openalex.org/W4235928131","doi":"https://doi.org/10.4203/ccp.106.126","title":"Stochastic Stability of the Inverted Pendulum subjected to Support Motion","display_name":"Stochastic Stability of the Inverted Pendulum subjected to Support Motion","publication_year":2014,"publication_date":"2014-08-20","ids":{"openalex":"https://openalex.org/W4235928131","doi":"https://doi.org/10.4203/ccp.106.126"},"language":"en","primary_location":{"id":"doi:10.4203/ccp.106.126","doi":"https://doi.org/10.4203/ccp.106.126","is_oa":false,"landing_page_url":"https://doi.org/10.4203/ccp.106.126","pdf_url":null,"source":{"id":"https://openalex.org/S4220651426","display_name":"Civil-comp proceedings","issn_l":"1759-3433","issn":["1759-3433"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1","poland-20"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Civil-Comp Proceedings","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","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/A5042509244","display_name":"C. Floris","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"C. Floris","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5042509244"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4618,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62911119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.6967999935150146,"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.6967999935150146,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.156700000166893,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.08470000326633453,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inverted-pendulum","display_name":"inverted pendulum","score":0.9380000233650208},{"id":"https://openalex.org/keywords/stochastic-stability","display_name":"stochastic stability","score":0.9929999709129333},{"id":"https://openalex.org/keywords/support-motion","display_name":"support motion","score":0.7580000162124634},{"id":"https://openalex.org/keywords/parametric-excitation","display_name":"parametric excitation","score":0.9819999933242798},{"id":"https://openalex.org/keywords/gaussian-processes","display_name":"Gaussian processes","score":0.6919999718666077},{"id":"https://openalex.org/keywords/almost-sure-stability","display_name":"almost sure stability","score":0.7059999704360962},{"id":"https://openalex.org/keywords/stability-boundaries","display_name":"stability boundaries","score":0.8289999961853027},{"id":"https://openalex.org/keywords/small-angle-approximation","display_name":"small-angle approximation","score":0.6190000176429749},{"id":"https://openalex.org/keywords/ground-motion","display_name":"ground motion","score":0.3709999918937683}],"concepts":[{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.7961781024932861},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.5478718280792236},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5132946372032166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48418405652046204},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4835483729839325},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2701491713523865},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1996576488018036},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16576462984085083},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.06552618741989136},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4203/ccp.106.126","doi":"https://doi.org/10.4203/ccp.106.126","is_oa":false,"landing_page_url":"https://doi.org/10.4203/ccp.106.126","pdf_url":null,"source":{"id":"https://openalex.org/S4220651426","display_name":"Civil-comp proceedings","issn_l":"1759-3433","issn":["1759-3433"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1","poland-20"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Civil-Comp Proceedings","raw_type":"proceedings-article"},{"id":"pmh:oai:re.public.polimi.it:11311/879154","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/879154","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2484065727","https://openalex.org/W4401486779","https://openalex.org/W2031889340","https://openalex.org/W2039794981","https://openalex.org/W4405927379","https://openalex.org/W1993532084","https://openalex.org/W2073832445","https://openalex.org/W2610402075","https://openalex.org/W2511753173","https://openalex.org/W2299148802"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,27,31,39,92,129,134,170,187],"concerned":[3],"with":[4,12],"the":[5,17,23,25,65,68,78,84,96,98,114,118,122,127,141,147,153,156,166,179,183],"stochastic":[6,45,69,138,145],"stability":[7,70,151,154,180,186],"of":[8,67,80,86,100,121,137,144],"an":[9],"inverted":[10],"pendulum":[11],"a":[13,20,34,43,52,74,135],"point":[14],"mass":[15],"at":[16,22],"top":[18],"and":[19,152,182],"spring":[21],"base;":[24],"bar":[26],"massless.":[28],"The":[29],"base":[30],"subjected":[32],"to":[33,41,73,83,175],"vertical":[35,53],"acceleration":[36],"A(t)":[37],"that":[38,94,106,132,172],"supposed":[40],"be":[42,57],"Gaussian":[44],"process.":[46],"A":[47],"line-like":[48],"structure":[49],"excited":[50],"by":[51],"ground":[54],"motion":[55,81,97,115],"can":[56],"idealized":[58],"in":[59,155,165,178],"this":[60,112],"way.":[61],"Without":[62],"simplifying":[63],"assumptions":[64],"study":[66],"gives":[71],"rise":[72],"non-trivial":[75],"problem":[76],"as":[77],"equation":[79,116],"belongs":[82],"class":[85],"damped":[87],"Mathieu":[88],"equations.":[89],"Thus,":[90],"it":[91,169],"assumed":[93],"during":[95],"angle":[99],"rotation":[101],"theta":[102,109],"remains":[103],"small":[104],"so":[105,131],"sin(theta)":[107],"=":[108],".":[110],"In":[111],"way,":[113],"assumes":[117],"classical":[119],"form":[120],"second":[123,157],"order":[124],"oscillator,":[125],"but":[126],"excitation":[128],"parametric":[130],"there":[133],"possibility":[136],"instability.":[139],"Among":[140],"different":[142],"definitions":[143],"stability,":[146],"almost":[148,184],"sure":[149,185],"(sample)":[150],"moments":[158],"are":[159,163],"considered":[160],"herein.":[161],"They":[162],"compared":[164],"numerical":[167],"analyses:":[168],"found":[171],"they":[173],"lead":[174],"notable":[176],"differences":[177],"boundaries":[181],"not":[188],"conservative.":[189]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2022-05-12T00:00:00"}
