{"id":"https://openalex.org/W4387455595","doi":"https://doi.org/10.1134/s0361768823020135","title":"Resonances and Periodic Motions of Atwood\u2019s Machine with Two Oscillating Weights","display_name":"Resonances and Periodic Motions of Atwood\u2019s Machine with Two Oscillating Weights","publication_year":2023,"publication_date":"2023-10-01","ids":{"openalex":"https://openalex.org/W4387455595","doi":"https://doi.org/10.1134/s0361768823020135"},"language":"en","primary_location":{"id":"doi:10.1134/s0361768823020135","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1134/s0361768823020135","pdf_url":null,"source":{"id":"https://openalex.org/S150218641","display_name":"Programming and Computer Software","issn_l":"0361-7688","issn":["0361-7688","1608-3261"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Programming and Computer Software","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/A5069166071","display_name":"A. N. Prokopenya","orcid":"https://orcid.org/0000-0001-9760-5185"},"institutions":[{"id":"https://openalex.org/I170230895","display_name":"Warsaw University of Life Sciences","ror":"https://ror.org/05srvzs48","country_code":"PL","type":"education","lineage":["https://openalex.org/I170230895"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"A. N. Prokopenya","raw_affiliation_strings":["Warsaw University of Life Sciences, 02-776, Warsaw, Poland","Warsaw University of Life Sciences, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Warsaw University of Life Sciences, 02-776, Warsaw, Poland","institution_ids":["https://openalex.org/I170230895"]},{"raw_affiliation_string":"Warsaw University of Life Sciences, Warsaw, Poland","institution_ids":["https://openalex.org/I170230895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069166071"],"corresponding_institution_ids":["https://openalex.org/I170230895"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12899361,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"5","first_page":"433","last_page":"440"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9994999766349792,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9994999766349792,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.991599977016449,"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/T11416","display_name":"Numerical methods for differential equations","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/omega","display_name":"Omega","score":0.6820484399795532},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.6703278422355652},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6450930237770081},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.6381658911705017},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6082984805107117},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5880458950996399},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.576364278793335},{"id":"https://openalex.org/keywords/equations-of-motion","display_name":"Equations of motion","score":0.5598630309104919},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5116684436798096},{"id":"https://openalex.org/keywords/resonance","display_name":"Resonance (particle physics)","score":0.49968791007995605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4941599667072296},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49299928545951843},{"id":"https://openalex.org/keywords/periodic-function","display_name":"Periodic function","score":0.4728030562400818},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.42094290256500244},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.34997105598449707},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.2717936336994171},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1826244592666626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17132258415222168},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07534044981002808}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6820484399795532},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.6703278422355652},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6450930237770081},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.6381658911705017},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6082984805107117},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5880458950996399},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.576364278793335},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.5598630309104919},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5116684436798096},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.49968791007995605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4941599667072296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49299928545951843},{"id":"https://openalex.org/C98644592","wikidata":"https://www.wikidata.org/wiki/Q184743","display_name":"Periodic function","level":2,"score":0.4728030562400818},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.42094290256500244},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34997105598449707},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2717936336994171},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1826244592666626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17132258415222168},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07534044981002808},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0361768823020135","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1134/s0361768823020135","pdf_url":null,"source":{"id":"https://openalex.org/S150218641","display_name":"Programming and Computer Software","issn_l":"0361-7688","issn":["0361-7688","1608-3261"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Programming and Computer Software","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":14,"referenced_works":["https://openalex.org/W1550473901","https://openalex.org/W1958809597","https://openalex.org/W1969156547","https://openalex.org/W1980277151","https://openalex.org/W1996121262","https://openalex.org/W2001720058","https://openalex.org/W2011946352","https://openalex.org/W2032926497","https://openalex.org/W2064871836","https://openalex.org/W2078534064","https://openalex.org/W2346726143","https://openalex.org/W2839316593","https://openalex.org/W3016819792","https://openalex.org/W3130319038"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W4205377127","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W4292947165","https://openalex.org/W3045121788","https://openalex.org/W3201655533","https://openalex.org/W3134442314","https://openalex.org/W2281248943"],"abstract_inverted_index":{"The":[0,93],"problem":[1],"of":[2,9,11,36,52,87,95,101,104,109],"constructing":[3],"periodic":[4,50],"solutions":[5,47,81,100],"to":[6],"the":[7,19,26,34,53,56,59,85,96,102,107,110,118],"equations":[8,32,103],"motion":[10,35,105],"Atwood\u2019s":[12],"machine":[13],"in":[14,25,63,84,89],"which":[15],"both":[16],"weights":[17,54],"have":[18],"same":[20],"mass":[21],"and":[22,41,73],"can":[23],"oscillate":[24],"vertical":[27],"plane":[28],"is":[29,78],"discussed.":[30],"Differential":[31],"governing":[33],"this":[37],"system":[38,121],"are":[39,62,75,82,115],"derived,":[40],"an":[42],"algorithm":[43],"for":[44],"calculating":[45],"their":[46],"that":[48,58],"determine":[49],"oscillations":[51],"under":[55],"condition":[57],"oscillation":[60],"frequencies":[61],"resonance":[64],"$$n{{\\omega":[65],"}_{1}}":[66],"=":[67],"m{{\\omega":[68],"}_{2}}$$":[69],",":[70],"where":[71],"n":[72],"m":[74],"natural":[76],"numbers,":[77],"proposed.":[79],"These":[80],"obtained":[83,111],"form":[86],"series":[88],"a":[90],"small":[91],"parameter.":[92],"comparison":[94],"results":[97],"with":[98],"numerical":[99],"confirm":[106],"validity":[108],"solutions.":[112],"All":[113],"computations":[114],"performed":[116],"using":[117],"computer":[119],"algebra":[120],"Wolfram":[122],"Mathematica.":[123]},"counts_by_year":[],"updated_date":"2026-01-23T23:20:30.427331","created_date":"2025-10-10T00:00:00"}
