{"id":"https://openalex.org/W2041376312","doi":"https://doi.org/10.1137/070704393","title":"The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods","display_name":"The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2041376312","doi":"https://doi.org/10.1137/070704393","mag":"2041376312"},"language":"en","primary_location":{"id":"doi:10.1137/070704393","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070704393","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11577/2266655","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008467121","display_name":"Elena Celledoni","orcid":"https://orcid.org/0000-0002-2863-2603"},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"E. Celledoni","raw_affiliation_strings":["Elena.Celledoni@math.ntnu.no and Niklas.Savstrom@math.ntnu.no#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Elena.Celledoni@math.ntnu.no and Niklas.Savstrom@math.ntnu.no#TAB#","institution_ids":["https://openalex.org/I204778367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015420361","display_name":"Francesco Fass\u00f2","orcid":"https://orcid.org/0000-0003-1043-3152"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"F. Fass\u00f2","raw_affiliation_strings":["fasso@math.unipd.it#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"fasso@math.unipd.it#TAB#","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015028204","display_name":"Niklas S\u00e4fstr\u00f6m","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. S\u00e4fstr\u00f6m","raw_affiliation_strings":["Department of Mathematical Sciences, NTNU, 7491 Trondheim, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, NTNU, 7491 Trondheim, Norway","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015777960","display_name":"Antonella Zanna","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Zanna","raw_affiliation_strings":["Antonella.Zanna@math.uib.no#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Antonella.Zanna@math.uib.no#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.4351,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.94172553,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"30","issue":"4","first_page":"2084","last_page":"2112"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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":0.9998999834060669,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9936000108718872,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.7374119758605957},{"id":"https://openalex.org/keywords/rigid-body","display_name":"Rigid body","score":0.7262262105941772},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7059301137924194},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5858249068260193},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.5661199688911438},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5655232667922974},{"id":"https://openalex.org/keywords/rigid-body-dynamics","display_name":"Rigid body dynamics","score":0.5579591393470764},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.5216844081878662},{"id":"https://openalex.org/keywords/machine-epsilon","display_name":"Machine epsilon","score":0.468219518661499},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43972715735435486},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36500078439712524},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.30406469106674194},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21945542097091675},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.20606577396392822}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7374119758605957},{"id":"https://openalex.org/C145980571","wikidata":"https://www.wikidata.org/wiki/Q192788","display_name":"Rigid body","level":2,"score":0.7262262105941772},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7059301137924194},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5858249068260193},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.5661199688911438},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5655232667922974},{"id":"https://openalex.org/C28461519","wikidata":"https://www.wikidata.org/wiki/Q2037529","display_name":"Rigid body dynamics","level":3,"score":0.5579591393470764},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5216844081878662},{"id":"https://openalex.org/C203739276","wikidata":"https://www.wikidata.org/wiki/Q1780355","display_name":"Machine epsilon","level":2,"score":0.468219518661499},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43972715735435486},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36500078439712524},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30406469106674194},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21945542097091675},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.20606577396392822},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070704393","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070704393","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:www.research.unipd.it:11577/2266655","is_oa":true,"landing_page_url":"http://hdl.handle.net/11577/2266655","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:www.research.unipd.it:11577/2266655","is_oa":true,"landing_page_url":"http://hdl.handle.net/11577/2266655","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1493432055","https://openalex.org/W1506846531","https://openalex.org/W1976207657","https://openalex.org/W1978463812","https://openalex.org/W1996160600","https://openalex.org/W1997231608","https://openalex.org/W2001515423","https://openalex.org/W2003158327","https://openalex.org/W2003161517","https://openalex.org/W2020958975","https://openalex.org/W2022218119","https://openalex.org/W2022733366","https://openalex.org/W2024942080","https://openalex.org/W2025030615","https://openalex.org/W2061411896","https://openalex.org/W2079572802","https://openalex.org/W2088842637","https://openalex.org/W2089590357","https://openalex.org/W2113557458","https://openalex.org/W2134565859","https://openalex.org/W2155579513","https://openalex.org/W2163257413","https://openalex.org/W2801179766","https://openalex.org/W2947056241","https://openalex.org/W2952827647","https://openalex.org/W4245463005"],"related_works":["https://openalex.org/W1547662599","https://openalex.org/W2613206230","https://openalex.org/W2948202761","https://openalex.org/W4233673530","https://openalex.org/W2499999313","https://openalex.org/W2329279984","https://openalex.org/W2917119513","https://openalex.org/W2084751898","https://openalex.org/W2165354764","https://openalex.org/W2914794850"],"abstract_inverted_index":{"This":[0],"article":[1],"investigates":[2],"the":[3,6,9,36,39,93,114],"use":[4],"of":[5,8,18,35,38,80,117],"computation":[7],"exact":[10,63],"free":[11,40],"rigid":[12,22,41,89,119],"body":[13,42],"motion":[14],"as":[15,92],"a":[16,78],"component":[17],"splitting":[19,107],"methods":[20],"for":[21,88],"bodies":[23],"subject":[24],"to":[25,55,66,113],"external":[26],"forces.":[27],"We":[28,58,76],"review":[29],"various":[30],"matrix":[31],"and":[32,49,52,69],"quaternion":[33],"representations":[34],"solution":[37],"equation":[43],"which":[44,61],"involve":[45],"Jacobi":[46],"ellipic":[47],"functions":[48],"elliptic":[50],"integrals":[51],"are":[53,62],"amenable":[54],"numerical":[56,82,99,115],"computations.":[57],"consider":[59],"implementations":[60],"(i.e.,":[64,71],"computed":[65],"machine":[67],"precision)":[68],"semiexact":[70],"approximated":[72],"via":[73],"quadrature":[74],"formulas).":[75],"perform":[77],"set":[79],"extensive":[81],"comparisons":[83],"with":[84,106],"state-of-the-art":[85],"geometrical":[86],"integrators":[87],"bodies,":[90],"such":[91],"preprocessed":[94],"discrete":[95],"Moser\u2013Veselov":[96],"method.":[97],"Our":[98],"simulations":[100],"indicate":[101],"that":[102],"these":[103],"techniques,":[104],"combined":[105],"methods,":[108],"can":[109],"be":[110],"favorably":[111],"applied":[112],"integration":[116],"torqued":[118],"bodies.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":31},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2016-06-24T00:00:00"}