{"id":"https://openalex.org/W2082227203","doi":"https://doi.org/10.1142/s0218127405013745","title":"GEOMETRY OF VIBRATIONAL STABILIZATION AND SOME APPLICATIONS","display_name":"GEOMETRY OF VIBRATIONAL STABILIZATION AND SOME APPLICATIONS","publication_year":2005,"publication_date":"2005-09-01","ids":{"openalex":"https://openalex.org/W2082227203","doi":"https://doi.org/10.1142/s0218127405013745","mag":"2082227203"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405013745","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405013745","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"MARK LEVI","raw_affiliation_strings":["Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054211978"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":0.9703,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.81104017,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":"09","first_page":"2747","last_page":"2756"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9833999872207642,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9833999872207642,"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/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.9660000205039978,"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/T10325","display_name":"Astro and Planetary Science","score":0.954200029373169,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonholonomic-system","display_name":"Nonholonomic system","score":0.7571291327476501},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.7058311700820923},{"id":"https://openalex.org/keywords/holonomic","display_name":"Holonomic","score":0.6763328909873962},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.6015787124633789},{"id":"https://openalex.org/keywords/holonomic-constraints","display_name":"Holonomic constraints","score":0.5459063649177551},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.4996044635772705},{"id":"https://openalex.org/keywords/pendulum","display_name":"Pendulum","score":0.48164477944374084},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.457193523645401},{"id":"https://openalex.org/keywords/double-pendulum","display_name":"Double pendulum","score":0.4520364999771118},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4500459134578705},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.4160272181034088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34103405475616455},{"id":"https://openalex.org/keywords/inverted-pendulum","display_name":"Inverted pendulum","score":0.33939260244369507},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.314363956451416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2855168581008911},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2662857472896576},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.0871107280254364}],"concepts":[{"id":"https://openalex.org/C138632511","wikidata":"https://www.wikidata.org/wiki/Q2478109","display_name":"Nonholonomic system","level":4,"score":0.7571291327476501},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.7058311700820923},{"id":"https://openalex.org/C2777964439","wikidata":"https://www.wikidata.org/wiki/Q5884201","display_name":"Holonomic","level":2,"score":0.6763328909873962},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6015787124633789},{"id":"https://openalex.org/C116721078","wikidata":"https://www.wikidata.org/wiki/Q1048005","display_name":"Holonomic constraints","level":2,"score":0.5459063649177551},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.4996044635772705},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.48164477944374084},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.457193523645401},{"id":"https://openalex.org/C167183279","wikidata":"https://www.wikidata.org/wiki/Q1243208","display_name":"Double pendulum","level":4,"score":0.4520364999771118},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4500459134578705},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4160272181034088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34103405475616455},{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.33939260244369507},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.314363956451416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2855168581008911},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2662857472896576},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.0871107280254364},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127405013745","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405013745","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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":22,"referenced_works":["https://openalex.org/W27988849","https://openalex.org/W1987482895","https://openalex.org/W1989082180","https://openalex.org/W2002488856","https://openalex.org/W2005151386","https://openalex.org/W2007347255","https://openalex.org/W2016005409","https://openalex.org/W2032262012","https://openalex.org/W2035039193","https://openalex.org/W2040583798","https://openalex.org/W2046890312","https://openalex.org/W2055499899","https://openalex.org/W2056304959","https://openalex.org/W2077198565","https://openalex.org/W2079996094","https://openalex.org/W2093441125","https://openalex.org/W2100020546","https://openalex.org/W2240200704","https://openalex.org/W2487275477","https://openalex.org/W3099736308","https://openalex.org/W3127727104","https://openalex.org/W4242824945"],"related_works":["https://openalex.org/W2154502479","https://openalex.org/W2127776540","https://openalex.org/W76235543","https://openalex.org/W45593259","https://openalex.org/W641237144","https://openalex.org/W1973747674","https://openalex.org/W4378942199","https://openalex.org/W2370863384","https://openalex.org/W2018918536","https://openalex.org/W2183446508"],"abstract_inverted_index":{"This":[0,168],"paper":[1],"gives":[2],"a":[3,31,40,71,103,106,129,174,197,204],"short":[4],"overview":[5],"of":[6,9,17,21,61,79,105,156,165,190,200],"various":[7],"applications":[8],"stabilization":[10],"by":[11,39],"vibration,":[12],"along":[13,128],"with":[14,96,173],"the":[15,18,26,58,77,80,86,90,94,119,134,140,144,150,157,162,166,171,178,188],"exposition":[16],"geometrical":[19],"mechanism":[20],"this":[22],"phenomenon.":[23],"More":[24],"specifically,":[25],"following":[27],"observation":[28,101],"is":[29,102,148,152,207],"described:":[30],"rapidly":[32,53],"vibrated":[33,54],"holonomic":[34],"system":[35],"can":[36],"be":[37],"approximated":[38],"certain":[41],"associated":[42,63],"nonholonomic":[43,65],"system.":[44],"It":[45],"turns":[46],"out":[47],"that":[48],"effective":[49,91,163],"forces":[50,60],"in":[51,116,161,193],"some":[52],"(holonomic)":[55],"systems":[56],"are":[57],"constraint":[59],"an":[62],"auxiliary":[64],"constraint.":[66],"In":[67],"particular,":[68],"we":[69],"review":[70],"simple":[72],"but":[73],"remarkable":[74],"connection":[75],"between":[76,111,170],"curvature":[78],"pursuit":[81],"curve":[82],"(the":[83],"tractrix)":[84],"on":[85,93,203],"one":[87],"hand":[88],"and":[89,132,177],"force":[92],"pendulum":[95,120,172],"vibrating":[97,205],"support.":[98],"The":[99,146,154],"latter":[100,151],"part":[104],"recently":[107],"discovered":[108],"close":[109],"relationship":[110,169],"two":[112],"standard":[113],"classical":[114],"problems":[115],"mechanics:":[117],"(1)":[118],"whose":[121],"suspension":[122],"point":[123],"executes":[124],"fast":[125],"periodic":[126],"motion":[127,164],"given":[130],"curve,":[131],"(2)":[133],"Chaplygin":[135,179],"skate":[136,158,180],"(known":[137],"also":[138],"as":[139,187],"Prytz":[141],"planimeter,":[142],"or":[143],"\"bicycle\").":[145],"former":[147],"holonomic,":[149],"nonholonomic.":[153],"holonomy":[155],"shows":[159],"up":[160],"pendulum.":[167],"twirled":[175],"pivot":[176],"has":[181],"somewhat":[182],"unexpected":[183],"physical":[184],"manifestations,":[185],"such":[186],"drift":[189],"suspended":[191],"particles":[192],"acoustic":[194],"waves.":[195],"Finally,":[196],"higher-dimensional":[198],"example":[199],"\"geodesic":[201],"motion\"":[202],"surface":[206],"described.":[208]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}