{"id":"https://openalex.org/W2196494282","doi":"https://doi.org/10.1109/iceee.2015.7357933","title":"Ziegler paradox and periodic coefficient differential equations","display_name":"Ziegler paradox and periodic coefficient differential equations","publication_year":2015,"publication_date":"2015-10-01","ids":{"openalex":"https://openalex.org/W2196494282","doi":"https://doi.org/10.1109/iceee.2015.7357933","mag":"2196494282"},"language":"en","primary_location":{"id":"doi:10.1109/iceee.2015.7357933","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iceee.2015.7357933","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 12th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)","raw_type":"proceedings-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/A5101616771","display_name":"Carlos Franco","orcid":"https://orcid.org/0000-0001-5556-4602"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Carlos Franco","raw_affiliation_strings":["DCA CINVESTAV, Mexico, D.F"],"affiliations":[{"raw_affiliation_string":"DCA CINVESTAV, Mexico, D.F","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108500980","display_name":"Joaqu\u0131\u0301n Collado","orcid":null},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Joaquin Collado","raw_affiliation_strings":["DCA CINVESTAV, Mexico, D.F"],"affiliations":[{"raw_affiliation_string":"DCA CINVESTAV, Mexico, D.F","institution_ids":["https://openalex.org/I68368234"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101616771"],"corresponding_institution_ids":["https://openalex.org/I68368234"],"apc_list":null,"apc_paid":null,"fwci":0.628,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75323383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12197","display_name":"Brake Systems and Friction Analysis","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/T12197","display_name":"Brake Systems and Friction Analysis","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9598000049591064,"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/mathieu-function","display_name":"Mathieu function","score":0.5409773588180542},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5314962267875671},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5013141632080078},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45821613073349},{"id":"https://openalex.org/keywords/mechanical-system","display_name":"Mechanical system","score":0.42875421047210693},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.36135178804397583},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3526079058647156},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21472421288490295}],"concepts":[{"id":"https://openalex.org/C157097347","wikidata":"https://www.wikidata.org/wiki/Q1908689","display_name":"Mathieu function","level":2,"score":0.5409773588180542},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5314962267875671},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5013141632080078},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45821613073349},{"id":"https://openalex.org/C171912257","wikidata":"https://www.wikidata.org/wiki/Q11019","display_name":"Mechanical system","level":2,"score":0.42875421047210693},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36135178804397583},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3526079058647156},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21472421288490295},{"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:10.1109/iceee.2015.7357933","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iceee.2015.7357933","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 12th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)","raw_type":"proceedings-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":[],"funders":[{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W89395536","https://openalex.org/W1662091431","https://openalex.org/W1966706206","https://openalex.org/W2015497683","https://openalex.org/W2062434330","https://openalex.org/W2071515585","https://openalex.org/W2095082890","https://openalex.org/W2135266305","https://openalex.org/W2321433934","https://openalex.org/W2497554230","https://openalex.org/W3094017215","https://openalex.org/W3106046485","https://openalex.org/W4240249953","https://openalex.org/W4247524324"],"related_works":["https://openalex.org/W1968091714","https://openalex.org/W2482220259","https://openalex.org/W4248360533","https://openalex.org/W1976863281","https://openalex.org/W2740883965","https://openalex.org/W2073589779","https://openalex.org/W2019399828","https://openalex.org/W4282976747","https://openalex.org/W4255217649","https://openalex.org/W4205358721"],"abstract_inverted_index":{"The":[0,44],"Ziegler":[1],"paradox":[2,36],"establishes":[3],"that:":[4],"given":[5],"a":[6,21],"stable":[7],"non-conservative":[8],"mechanical":[9],"system":[10,26],"with":[11,39],"at":[12],"least":[13],"two":[14],"degrees":[15],"of":[16,42,53],"freedom,":[17],"if":[18],"we":[19,33],"add":[20],"small":[22],"damping":[23],"the":[24,51,54,62],"resulting":[25],"may":[27],"be":[28],"unstable.":[29],"In":[30],"this":[31,35],"paper":[32],"extend":[34],"for":[37,61],"systems":[38],"one":[40],"degree":[41],"freedom.":[43],"result":[45],"is":[46],"based":[47],"on":[48],"changing":[49],"periodically":[50],"coefficients":[52],"system.":[55],"Some":[56],"numerical":[57],"results":[58],"are":[59],"presented":[60],"Mathieu's":[63],"and":[64],"Meissner's":[65],"equations.":[66]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}