{"id":"https://openalex.org/W7225320900","doi":"https://doi.org/10.21203/rs.3.rs-11415393/v1","title":"The period function at a C 1 switching level: loss of smoothness and a critical period for a pendulum with unilateral elastic stops","display_name":"The period function at a C 1 switching level: loss of smoothness and a critical period for a pendulum with unilateral elastic stops","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225320900","doi":"https://doi.org/10.21203/rs.3.rs-11415393/v1"},"language":"en","primary_location":{"id":"doi:10.21203/rs.3.rs-11415393/v1","doi":"https://doi.org/10.21203/rs.3.rs-11415393/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11415393/v1","pdf_url":"https://www.researchsquare.com/article/rs-11415393/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Research Square","raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.researchsquare.com/article/rs-11415393/latest.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001448355","display_name":"Alvaro Humberto Salas","orcid":"https://orcid.org/0000-0001-9343-6062","observed_orcids":["https://orcid.org/0000-0001-9343-6062"]},"institutions":[{"id":"https://openalex.org/I36243813","display_name":"Universidad Nacional de Colombia","ror":"https://ror.org/059yx9a68","country_code":"CO","type":"education","lineage":["https://openalex.org/I36243813"]}],"countries":["CO"],"is_corresponding":true,"raw_author_name":"Alvaro H. Salas","raw_affiliation_strings":["Universidad Nacional de Colombia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad Nacional de Colombia","institution_ids":["https://openalex.org/I36243813"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001448355"],"corresponding_institution_ids":["https://openalex.org/I36243813"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.7724999785423279,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.7724999785423279,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.11999999731779099,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.044599998742341995,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/period-function","display_name":"period function","score":0.9990000128746033},{"id":"https://openalex.org/keywords/critical-period","display_name":"critical period","score":0.9750000238418579},{"id":"https://openalex.org/keywords/pendulum","display_name":"pendulum","score":0.7670000195503235},{"id":"https://openalex.org/keywords/piecewise-smooth-systems","display_name":"piecewise-smooth systems","score":0.3319999873638153}],"concepts":[{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.6948999762535095},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6868000030517578},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.667900025844574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6292999982833862},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5570999979972839},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5446000099182129},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5314000248908997},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.4674000144004822},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4375999867916107},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4131999909877777},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36660000681877136},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3571999967098236},{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.3140000104904175},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.30649998784065247}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.21203/rs.3.rs-11415393/v1","doi":"https://doi.org/10.21203/rs.3.rs-11415393/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11415393/v1","pdf_url":"https://www.researchsquare.com/article/rs-11415393/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Research Square","raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.21203/rs.3.rs-11415393/v1","doi":"https://doi.org/10.21203/rs.3.rs-11415393/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11415393/v1","pdf_url":"https://www.researchsquare.com/article/rs-11415393/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Research Square","raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321458","display_name":"Universidad Nacional de Colombia","ror":"https://ror.org/059yx9a68"},{"id":"https://openalex.org/F4320335258","display_name":"Universidad Nacional de Colombia, Sede Manizales","ror":"https://ror.org/059yx9a68"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225320900.pdf","grobid_xml":"https://content.openalex.org/works/W7225320900.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1558079603","https://openalex.org/W2011227277","https://openalex.org/W2030450697","https://openalex.org/W4206179747","https://openalex.org/W4255896881"],"related_works":["https://openalex.org/W7100201726","https://openalex.org/W7212052569","https://openalex.org/W7096523061","https://openalex.org/W4403336676","https://openalex.org/W2332476769","https://openalex.org/W2076623540","https://openalex.org/W2088006715","https://openalex.org/W2781997544","https://openalex.org/W4404861335","https://openalex.org/W2285739194"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"study":[2],"the":[3,25,63],"period":[4,64],"function":[5],"of":[6],"planar":[7],"conservative":[8],"systems\u00a8xsystems\u00a8":[9],"systems\u00a8x":[10],"+":[11],"W":[12,42,51],"\u2032":[13,43],"(x)":[14],"=":[15,38,46,68],"0":[16,49],"whose":[17],"potential":[18],"is":[19],"C":[20],"1":[21],"but":[22],"piecewise":[23],"analytic,":[24],"switching":[26],"being":[27],"caused":[28],"by":[29,54],"a":[30],"unilateral":[31],"elastic":[32],"constraint":[33],"that":[34,62],"engages":[35],"at":[36,56],"x":[37,39,57],"g.":[40],"If":[41],"(x":[44],"g)":[45],"d":[47],">":[48],"and":[50],"\u2032\u2032":[52],"jumps":[53],"J":[55],"g":[58],",":[59],"we":[60],"prove":[61],"satisfies":[65],"T":[66,69],"(h)":[67,70],"\u2212":[71],"4":[72]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-06T00:00:00"}