{"id":"https://openalex.org/W3157651445","doi":"https://doi.org/10.1142/s0218127421500759","title":"Jacobi Stability Analysis and the Onset of Chaos in a Two-Degree-of-Freedom Mechanical System","display_name":"Jacobi Stability Analysis and the Onset of Chaos in a Two-Degree-of-Freedom Mechanical System","publication_year":2021,"publication_date":"2021-04-01","ids":{"openalex":"https://openalex.org/W3157651445","doi":"https://doi.org/10.1142/s0218127421500759","mag":"3157651445"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127421500759","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421500759","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/A5044274380","display_name":"Fanrui Wang","orcid":"https://orcid.org/0000-0002-3628-5437"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fanrui Wang","raw_affiliation_strings":["School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China","institution_ids":["https://openalex.org/I3124059619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057382261","display_name":"Ting Liu","orcid":"https://orcid.org/0000-0003-3458-6567"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ting Liu","raw_affiliation_strings":["School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China","institution_ids":["https://openalex.org/I3124059619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083808886","display_name":"\u041d. \u0412. \u041a\u0443\u0437\u043d\u0435\u0446\u043e\u0432","orcid":"https://orcid.org/0000-0002-6474-9657"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I94722563","display_name":"University of Jyv\u00e4skyl\u00e4","ror":"https://ror.org/05n3dz165","country_code":"FI","type":"education","lineage":["https://openalex.org/I94722563"]}],"countries":["FI","RU"],"is_corresponding":false,"raw_author_name":"Nikolay V. Kuznetsov","raw_affiliation_strings":["Department of Mathematical Information Technology, University of Jyv\u00e4skyl\u00e4, Jyv\u00e4skyl\u00e4, Finland","Faculty of Mathematics and Mechanics, St. Petersburg State University, Peterhof, St. Petersburg, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Information Technology, University of Jyv\u00e4skyl\u00e4, Jyv\u00e4skyl\u00e4, Finland","institution_ids":["https://openalex.org/I94722563"]},{"raw_affiliation_string":"Faculty of Mathematics and Mechanics, St. Petersburg State University, Peterhof, St. Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075850521","display_name":"Zhouchao Wei","orcid":"https://orcid.org/0000-0001-6981-748X"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]},{"id":"https://openalex.org/I3125743391","display_name":"China University of Geosciences (Beijing)","ror":"https://ror.org/04q6c7p66","country_code":"CN","type":"education","lineage":["https://openalex.org/I3125743391"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhouchao Wei","raw_affiliation_strings":["School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China","Zhejiang Institute, China University of Geosciences, Hangzhou, Zhejiang 311305, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China","institution_ids":["https://openalex.org/I3124059619"]},{"raw_affiliation_string":"Zhejiang Institute, China University of Geosciences, Hangzhou, Zhejiang 311305, P. R. China","institution_ids":["https://openalex.org/I3125743391"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5075850521"],"corresponding_institution_ids":["https://openalex.org/I3124059619","https://openalex.org/I3125743391"],"apc_list":null,"apc_paid":null,"fwci":1.6172,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.82586992,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"31","issue":"05","first_page":"2150075","last_page":"2150075"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9962000250816345,"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"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9962000250816345,"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"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9943000078201294,"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"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9901000261306763,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7285212278366089},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6458180546760559},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6244306564331055},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6107563972473145},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.5675268173217773},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5549354553222656},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.5425949096679688},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49938225746154785},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.45496755838394165},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.45428088307380676},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.4105919599533081},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3534356355667114},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.25763046741485596},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20030122995376587},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15007176995277405},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1499314308166504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13630664348602295}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7285212278366089},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6458180546760559},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6244306564331055},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6107563972473145},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.5675268173217773},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5549354553222656},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.5425949096679688},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49938225746154785},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.45496755838394165},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.45428088307380676},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.4105919599533081},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3534356355667114},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.25763046741485596},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20030122995376587},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15007176995277405},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1499314308166504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13630664348602295},{"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/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127421500759","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421500759","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":[{"id":"https://metadata.un.org/sdg/16","score":0.8199999928474426,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G3727335406","display_name":null,"funder_award_id":"11772306","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5510970894","display_name":null,"funder_award_id":"LY20A020001","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1966466493","https://openalex.org/W1986518553","https://openalex.org/W2024191249","https://openalex.org/W2037682746","https://openalex.org/W2055482981","https://openalex.org/W2069166809","https://openalex.org/W2069436097","https://openalex.org/W2103598023","https://openalex.org/W2109185530","https://openalex.org/W2169982364","https://openalex.org/W2261060202","https://openalex.org/W2341495304","https://openalex.org/W2345501397","https://openalex.org/W2407346498","https://openalex.org/W2408502140","https://openalex.org/W2463344096","https://openalex.org/W2477618228","https://openalex.org/W2540229836","https://openalex.org/W2577900305","https://openalex.org/W2587436369","https://openalex.org/W2601279175","https://openalex.org/W2602396255","https://openalex.org/W2613285212","https://openalex.org/W2626365245","https://openalex.org/W2752337041","https://openalex.org/W2801336041","https://openalex.org/W2893121555","https://openalex.org/W2948447754","https://openalex.org/W2953577307","https://openalex.org/W2960095010","https://openalex.org/W2963011325","https://openalex.org/W2963175336","https://openalex.org/W2964079314","https://openalex.org/W2975098162","https://openalex.org/W3008282890","https://openalex.org/W3011923508","https://openalex.org/W3098289590","https://openalex.org/W3105549322","https://openalex.org/W4214820013","https://openalex.org/W4232785643"],"related_works":["https://openalex.org/W2351399966","https://openalex.org/W646915967","https://openalex.org/W2062572728","https://openalex.org/W3043043274","https://openalex.org/W2009483907","https://openalex.org/W1615168010","https://openalex.org/W2058823188","https://openalex.org/W3134744058","https://openalex.org/W1970933145","https://openalex.org/W2774064828"],"abstract_inverted_index":{"In":[0,84],"this":[1],"paper,":[2],"the":[3,14,25,40,52,56,60,76,86,96],"Jacobi":[4,26,43],"stability":[5,27,44,47],"of":[6,17,28,42,59,78,98],"a":[7,32],"two-degree-of-freedom":[8],"mechanical":[9],"system":[10],"is":[11],"studied":[12],"by":[13,35],"innovative":[15],"application":[16],"KCC-theory,":[18],"namely":[19],"differential":[20],"geometric":[21,37],"methods.":[22],"We":[23,54],"discuss":[24],"two":[29,64],"equilibria":[30,65],"and":[31,45,70,73,90],"periodic":[33],"orbit":[34],"constructing":[36],"invariants.":[38],"Both":[39],"regions":[41],"Lyapunov":[46],"are":[48,92],"presented":[49],"to":[50,81,103],"show":[51],"difference.":[53],"draw":[55],"phase":[57],"portraits":[58],"deviation":[61,79],"vector":[62,80],"near":[63],"under":[66],"specific":[67],"parameter":[68],"values":[69],"initial":[71,82],"conditions,":[72],"point":[74],"out":[75],"sensitivity":[77],"conditions.":[83],"addition,":[85],"corresponding":[87],"instability":[88],"exponent":[89],"curvature":[91],"applicable":[93],"for":[94],"predicting":[95],"onset":[97],"chaos,":[99],"which":[100],"help":[101],"us":[102],"detect":[104],"chaotic":[105],"behaviors":[106],"quantitatively.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}