{"id":"https://openalex.org/W2267045159","doi":"https://doi.org/10.1109/cdc.2015.7403164","title":"Global formulations of Lagrangian and Hamiltonian mechanics on two-spheres","display_name":"Global formulations of Lagrangian and Hamiltonian mechanics on two-spheres","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2267045159","doi":"https://doi.org/10.1109/cdc.2015.7403164","mag":"2267045159"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2015.7403164","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7403164","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1503.02620","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020132536","display_name":"Taeyoung Lee","orcid":"https://orcid.org/0000-0003-4982-4150"},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Taeyoung Lee","raw_affiliation_strings":["Mechanical and Aerospace Engineering, George Washington University, Washington DC","Mechanical and Aerospace Engineering, George Washington University, 20052, United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical and Aerospace Engineering, George Washington University, Washington DC","institution_ids":["https://openalex.org/I193531525"]},{"raw_affiliation_string":"Mechanical and Aerospace Engineering, George Washington University, 20052, United States of America","institution_ids":["https://openalex.org/I193531525"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047012686","display_name":"Melvin Leok","orcid":"https://orcid.org/0000-0002-8326-0830"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Melvin Leok","raw_affiliation_strings":["Mathematics, University of California at San Diego, La Jolla, CA","Mathematics, University of California at San Diego, La Jolla, 92093, United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics, University of California at San Diego, La Jolla, CA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Mathematics, University of California at San Diego, La Jolla, 92093, United States of America","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018682629","display_name":"N. Harris McClamroch","orcid":"https://orcid.org/0000-0002-7536-5659"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"N. Harris McClamroch","raw_affiliation_strings":["Aerospace Engineering, University of Michigan, Ann Arbor, MI","Aerospace Engineering, University of Michigan, Ann Arbor, 48109, United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aerospace Engineering, University of Michigan, Ann Arbor, MI","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Aerospace Engineering, University of Michigan, Ann Arbor, 48109, United States of America","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":"70","issue":null,"first_page":"6010","last_page":"6015"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9979000091552734,"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":0.9979000091552734,"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":0.9926999807357788,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.989300012588501,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.7679781913757324},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.7297790050506592},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.706010103225708},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.6714911460876465},{"id":"https://openalex.org/keywords/equations-of-motion","display_name":"Equations of motion","score":0.6264426708221436},{"id":"https://openalex.org/keywords/hamiltonian-mechanics","display_name":"Hamiltonian mechanics","score":0.6089115738868713},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.5768904685974121},{"id":"https://openalex.org/keywords/euler\u2013lagrange-equation","display_name":"Euler\u2013Lagrange equation","score":0.555108368396759},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46431753039360046},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.44162338972091675},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3373655676841736},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32506197690963745},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.12863677740097046},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07782915234565735}],"concepts":[{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.7679781913757324},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.7297790050506592},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.706010103225708},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6714911460876465},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.6264426708221436},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.6089115738868713},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.5768904685974121},{"id":"https://openalex.org/C2776392105","wikidata":"https://www.wikidata.org/wiki/Q875744","display_name":"Euler\u2013Lagrange equation","level":3,"score":0.555108368396759},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46431753039360046},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.44162338972091675},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3373655676841736},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32506197690963745},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.12863677740097046},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07782915234565735},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/cdc.2015.7403164","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7403164","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1503.02620","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.02620","pdf_url":"https://arxiv.org/pdf/1503.02620","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2267045159","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1503.02620.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.720.8781","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.720.8781","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucsd.edu/%7Emleok/pdf/LeLeMc2015_gfsph.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1503.02620","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1503.02620","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1503.02620","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.02620","pdf_url":"https://arxiv.org/pdf/1503.02620","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2267045159.pdf"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1524590822","https://openalex.org/W1555780618","https://openalex.org/W2012998314","https://openalex.org/W2071462623","https://openalex.org/W2143769694","https://openalex.org/W2575736220","https://openalex.org/W2962875223","https://openalex.org/W3217246742","https://openalex.org/W4388322878","https://openalex.org/W6817041117"],"related_works":["https://openalex.org/W2962875223","https://openalex.org/W2952382426","https://openalex.org/W2804174466","https://openalex.org/W2074250356","https://openalex.org/W3018046963","https://openalex.org/W1615500270","https://openalex.org/W807185958","https://openalex.org/W2996978246","https://openalex.org/W1553596068","https://openalex.org/W1546120426","https://openalex.org/W3103727357","https://openalex.org/W2998099316","https://openalex.org/W1972299755","https://openalex.org/W2463874101","https://openalex.org/W1612417119","https://openalex.org/W3163692405","https://openalex.org/W1422718562","https://openalex.org/W3028476950","https://openalex.org/W1532215532","https://openalex.org/W2362548749"],"abstract_inverted_index":{"This":[0],"paper":[1],"provides":[2],"global":[3,90],"formulations":[4,55],"of":[5,15,19,23,50,56,69,74,88],"Lagrangian":[6,57],"and":[7,26,47,58,80,86],"Hamiltonian":[8,59],"variational":[9],"dynamics":[10,60],"evolving":[11],"on":[12,35,39],"the":[13,67,89],"product":[14],"an":[16],"arbitrary":[17],"number":[18],"two-spheres.":[20],"Four":[21],"types":[22],"Euler-Lagrange":[24],"equations":[25,28,49,73],"Hamilton's":[27],"are":[29,61,77,82],"developed":[30],"in":[31,63,72,84],"a":[32],"coordinate-free":[33],"fashion":[34],"two-spheres,":[36,70],"without":[37],"relying":[38],"local":[40],"parameterizations":[41],"that":[42,64,76],"may":[43],"lead":[44],"to":[45],"singularities":[46],"cumbersome":[48],"motion.":[51],"The":[52],"proposed":[53],"intrinsic":[54],"novel":[62],"they":[65,81],"incorporate":[66],"geometry":[68],"resulting":[71],"motion":[75],"expressed":[78],"compactly,":[79],"useful":[83],"analysis":[85],"computation":[87],"dynamics.":[91]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
