{"id":"https://openalex.org/W4295211092","doi":"https://doi.org/10.3390/e24091269","title":"Dynamics and Entropy Analysis of a Frictionally Loaded Pendulum","display_name":"Dynamics and Entropy Analysis of a Frictionally Loaded Pendulum","publication_year":2022,"publication_date":"2022-09-09","ids":{"openalex":"https://openalex.org/W4295211092","doi":"https://doi.org/10.3390/e24091269","pmid":"https://pubmed.ncbi.nlm.nih.gov/36141155"},"language":"en","primary_location":{"id":"doi:10.3390/e24091269","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24091269","pdf_url":"https://www.mdpi.com/1099-4300/24/9/1269/pdf?version=1662711981","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/9/1269/pdf?version=1662711981","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063752443","display_name":"Grzegorz Litak","orcid":"https://orcid.org/0000-0002-9647-8345"},"institutions":[{"id":"https://openalex.org/I8264552","display_name":"Lublin University of Technology","ror":"https://ror.org/024zjzd49","country_code":"PL","type":"education","lineage":["https://openalex.org/I8264552"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Grzegorz Litak","raw_affiliation_strings":["Department of Automation, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland"],"raw_orcid":"https://orcid.org/0000-0002-9647-8345","affiliations":[{"raw_affiliation_string":"Department of Automation, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland","institution_ids":["https://openalex.org/I8264552"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050071481","display_name":"Marek Borowiec","orcid":"https://orcid.org/0000-0001-5986-5365"},"institutions":[{"id":"https://openalex.org/I8264552","display_name":"Lublin University of Technology","ror":"https://ror.org/024zjzd49","country_code":"PL","type":"education","lineage":["https://openalex.org/I8264552"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marek Borowiec","raw_affiliation_strings":["Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland"],"raw_orcid":"https://orcid.org/0000-0001-5986-5365","affiliations":[{"raw_affiliation_string":"Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland","institution_ids":["https://openalex.org/I8264552"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056829256","display_name":"Krzysztof D\u0105bek","orcid":null},"institutions":[{"id":"https://openalex.org/I8264552","display_name":"Lublin University of Technology","ror":"https://ror.org/024zjzd49","country_code":"PL","type":"education","lineage":["https://openalex.org/I8264552"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Krzysztof Da\u0327bek","raw_affiliation_strings":["Department of Automation, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland","institution_ids":["https://openalex.org/I8264552"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063752443"],"corresponding_institution_ids":["https://openalex.org/I8264552"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3754,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57367498,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"24","issue":"9","first_page":"1269","last_page":"1269"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.989799976348877,"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/T10244","display_name":"Chaos control and synchronization","score":0.989799976348877,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.963699996471405,"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/T10320","display_name":"Neural Networks and Applications","score":0.9539999961853027,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6946462392807007},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.6443819999694824},{"id":"https://openalex.org/keywords/pendulum","display_name":"Pendulum","score":0.537681519985199},{"id":"https://openalex.org/keywords/double-pendulum","display_name":"Double pendulum","score":0.5094678997993469},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5006511211395264},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.45297425985336304},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.43229788541793823},{"id":"https://openalex.org/keywords/froude-number","display_name":"Froude number","score":0.42378658056259155},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.397968590259552},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.38561999797821045},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37479740381240845},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31004834175109863},{"id":"https://openalex.org/keywords/inverted-pendulum","display_name":"Inverted pendulum","score":0.2926231622695923},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25901323556900024},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.20004883408546448},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1342136263847351},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08566927909851074}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6946462392807007},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.6443819999694824},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.537681519985199},{"id":"https://openalex.org/C167183279","wikidata":"https://www.wikidata.org/wiki/Q1243208","display_name":"Double pendulum","level":4,"score":0.5094678997993469},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5006511211395264},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.45297425985336304},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.43229788541793823},{"id":"https://openalex.org/C206835866","wikidata":"https://www.wikidata.org/wiki/Q273090","display_name":"Froude number","level":3,"score":0.42378658056259155},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.397968590259552},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.38561999797821045},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37479740381240845},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31004834175109863},{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.2926231622695923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25901323556900024},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.20004883408546448},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1342136263847351},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08566927909851074},{"id":"https://openalex.org/C2777871205","wikidata":"https://www.wikidata.org/wiki/Q100926628","display_name":"Breakup","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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":5,"locations":[{"id":"doi:10.3390/e24091269","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24091269","pdf_url":"https://www.mdpi.com/1099-4300/24/9/1269/pdf?version=1662711981","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:36141155","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36141155","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:04605cd3f93f4872b61902727e3b1378","is_oa":true,"landing_page_url":"https://doaj.org/article/04605cd3f93f4872b61902727e3b1378","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 9, p 1269 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/9/1269/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24091269","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 24; Issue 9; Pages: 1269","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9497587","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9497587","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24091269","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24091269","pdf_url":"https://www.mdpi.com/1099-4300/24/9/1269/pdf?version=1662711981","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4295211092.pdf","grobid_xml":"https://content.openalex.org/works/W4295211092.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1734021823","https://openalex.org/W1862394037","https://openalex.org/W1959913976","https://openalex.org/W1993017947","https://openalex.org/W1995875735","https://openalex.org/W2001065117","https://openalex.org/W2039771276","https://openalex.org/W2041287404","https://openalex.org/W2059851411","https://openalex.org/W2061237322","https://openalex.org/W2065546200","https://openalex.org/W2077204677","https://openalex.org/W2093266575","https://openalex.org/W2118183148","https://openalex.org/W2133849899","https://openalex.org/W2138311862","https://openalex.org/W2143091024","https://openalex.org/W2162800060","https://openalex.org/W2554171173","https://openalex.org/W2878523266","https://openalex.org/W2972286008","https://openalex.org/W2990988619","https://openalex.org/W3103942061","https://openalex.org/W3128808603","https://openalex.org/W3201289234","https://openalex.org/W4214507140","https://openalex.org/W4280555821","https://openalex.org/W6677760164","https://openalex.org/W6767687350"],"related_works":["https://openalex.org/W2051721081","https://openalex.org/W1963494060","https://openalex.org/W2912842457","https://openalex.org/W3016776681","https://openalex.org/W2293773556","https://openalex.org/W2149145472","https://openalex.org/W3090237748","https://openalex.org/W2378000718","https://openalex.org/W4390816033","https://openalex.org/W2527650984"],"abstract_inverted_index":{"We":[0,25,50],"use":[1],"friction":[2],"to":[3,15,21,73],"simultaneously":[4],"damp":[5],"and":[6,35,59],"excite":[7],"a":[8,16,22],"pendulum":[9,13],"system.":[10],"A":[11,43],"Froude":[12],"attached":[14],"suspension":[17],"shaft":[18],"is":[19],"subjected":[20],"frictional":[23],"load.":[24],"investigate":[26],"two":[27],"types":[28],"of":[29,31],"response":[30],"the":[32,40,52,63,70,75],"system:":[33],"regular":[34],"chaotic":[36,45],"responses,":[37],"depending":[38],"on":[39],"excitation":[41],"frequency.":[42],"transient":[44],"solution":[46],"was":[47,67],"also":[48],"obtained.":[49],"identify":[51],"motions":[53],"using":[54],"phase":[55],"portraits,":[56],"Poincar\u00e9":[57],"maps,":[58],"Fourier":[60],"spectra.":[61],"Finally,":[62],"composite":[64],"multiscaled":[65],"entropy":[66],"estimated":[68],"for":[69],"specified":[71],"cases":[72],"confirm":[74],"preliminary":[76],"classification.":[77]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}