{"id":"https://openalex.org/W4416829570","doi":"https://doi.org/10.5206/mt.v5i4.22647","title":"Solving the Differential Equations for the Pendulum and the Cantilever side-by-side","display_name":"Solving the Differential Equations for the Pendulum and the Cantilever side-by-side","publication_year":2025,"publication_date":"2025-11-30","ids":{"openalex":"https://openalex.org/W4416829570","doi":"https://doi.org/10.5206/mt.v5i4.22647"},"language":null,"primary_location":{"id":"doi:10.5206/mt.v5i4.22647","is_oa":true,"landing_page_url":"https://doi.org/10.5206/mt.v5i4.22647","pdf_url":"https://mapletransactions.org/index.php/maple/article/download/22647/18522","source":{"id":"https://openalex.org/S4210220724","display_name":"Maple Transactions","issn_l":"2564-3029","issn":["2564-3029"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320378","host_organization_name":"University of Western Ontario Libraries","host_organization_lineage":["https://openalex.org/P4310320378"],"host_organization_lineage_names":["University of Western Ontario Libraries"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Maple Transactions","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://mapletransactions.org/index.php/maple/article/download/22647/18522","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053427490","display_name":"Christian Rathjen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christian Rathjen","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-1299-2391","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053427490"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.47873711,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.19709999859333038,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.19709999859333038,"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"}},{"id":"https://openalex.org/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.11469999700784683,"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/T13806","display_name":"Mathematical and Computational Methods","score":0.11420000344514847,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/cantilever","display_name":"Cantilever","score":0.7330999970436096},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5471000075340271},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.4993000030517578},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.4936000108718872},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.46160000562667847},{"id":"https://openalex.org/keywords/pendulum","display_name":"Pendulum","score":0.4300999939441681},{"id":"https://openalex.org/keywords/deflection","display_name":"Deflection (physics)","score":0.41589999198913574},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.3984000086784363},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.3596999943256378}],"concepts":[{"id":"https://openalex.org/C141354745","wikidata":"https://www.wikidata.org/wiki/Q17227","display_name":"Cantilever","level":2,"score":0.7330999970436096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6062999963760376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5745000243186951},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5471000075340271},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.4993000030517578},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.4936000108718872},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.46160000562667847},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.4300999939441681},{"id":"https://openalex.org/C2781355719","wikidata":"https://www.wikidata.org/wiki/Q2080698","display_name":"Deflection (physics)","level":2,"score":0.41589999198913574},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.3984000086784363},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.3596999943256378},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.35499998927116394},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3271999955177307},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C2780414537","wikidata":"https://www.wikidata.org/wiki/Q42292","display_name":"Maple","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C204854254","wikidata":"https://www.wikidata.org/wiki/Q303072","display_name":"Examples of differential equations","level":5,"score":0.3086000084877014},{"id":"https://openalex.org/C167183279","wikidata":"https://www.wikidata.org/wiki/Q1243208","display_name":"Double pendulum","level":4,"score":0.30320000648498535},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.3012999892234802},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.30059999227523804},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2906000018119812},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.272599995136261},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.27250000834465027},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C163105828","wikidata":"https://www.wikidata.org/wiki/Q2734005","display_name":"Integrating factor","level":5,"score":0.2540999948978424}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5206/mt.v5i4.22647","is_oa":true,"landing_page_url":"https://doi.org/10.5206/mt.v5i4.22647","pdf_url":"https://mapletransactions.org/index.php/maple/article/download/22647/18522","source":{"id":"https://openalex.org/S4210220724","display_name":"Maple Transactions","issn_l":"2564-3029","issn":["2564-3029"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320378","host_organization_name":"University of Western Ontario Libraries","host_organization_lineage":["https://openalex.org/P4310320378"],"host_organization_lineage_names":["University of Western Ontario Libraries"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Maple Transactions","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.5206/mt.v5i4.22647","is_oa":true,"landing_page_url":"https://doi.org/10.5206/mt.v5i4.22647","pdf_url":"https://mapletransactions.org/index.php/maple/article/download/22647/18522","source":{"id":"https://openalex.org/S4210220724","display_name":"Maple Transactions","issn_l":"2564-3029","issn":["2564-3029"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320378","host_organization_name":"University of Western Ontario Libraries","host_organization_lineage":["https://openalex.org/P4310320378"],"host_organization_lineage_names":["University of Western Ontario Libraries"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Maple Transactions","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4416829570.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,20],"oscillation":[1],"of":[2,8,71],"a":[3,9,59],"pendulum":[4],"and":[5,25,39,69,83],"the":[6,30,36,52,57],"deflection":[7],"cantilever":[10,58],"beam":[11],"can":[12],"be":[13],"modeled":[14],"by":[15,23],"non-linear":[16],"ordinary":[17],"differential":[18,37,74],"equations.":[19],"non-linearity":[21],"introduced":[22],"sine":[24],"cosine":[26],"expressions":[27],"make":[28],"solving":[29],"equations":[31,38,75],"analytically":[32],"unexpected":[33],"challenging.":[34],"Although":[35],"solutions":[40,61],"steps":[41],"are":[42,76],"very":[43],"similar,":[44],"only":[45],"an":[46],"explicit":[47],"solution":[48],"is":[49],"known":[50],"for":[51,56],"pendulum,":[53],"whereas":[54],"as":[55],"semi-analytical":[60],"requiring":[62],"numerical":[63],"methods":[64],"exist.":[65],"To":[66],"compare":[67],"similarities":[68],"differences":[70],"both":[72],"cases,":[73],"solved":[77],"side-by-side":[78],"using":[79],"exclusively":[80],"Maple":[81],"commands":[82],"techniques.":[84]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-11-30T00:00:00"}
