{"id":"https://openalex.org/W3159822925","doi":"https://doi.org/10.1137/19m128867x","title":"Rotations in Three Dimensions","display_name":"Rotations in Three Dimensions","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3159822925","doi":"https://doi.org/10.1137/19m128867x","mag":"3159822925"},"language":"en","primary_location":{"id":"doi:10.1137/19m128867x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m128867x","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M128867X","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/19M128867X","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010736038","display_name":"M. F. Maritz","orcid":"https://orcid.org/0000-0003-2766-8206"},"institutions":[{"id":"https://openalex.org/I26092322","display_name":"Stellenbosch University","ror":"https://ror.org/05bk57929","country_code":"ZA","type":"education","lineage":["https://openalex.org/I26092322"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Milton F. Maritz","raw_affiliation_strings":["\\dagger Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, Western Cape 7601, South Africa"],"affiliations":[{"raw_affiliation_string":"\\dagger Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, Western Cape 7601, South Africa","institution_ids":["https://openalex.org/I26092322"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010736038"],"corresponding_institution_ids":["https://openalex.org/I26092322"],"apc_list":null,"apc_paid":null,"fwci":0.3946,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.59067907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"63","issue":"2","first_page":"395","last_page":"404"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.7893999814987183,"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/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.7893999814987183,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40716350078582764}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40716350078582764}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m128867x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m128867x","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M128867X","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/19m128867x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m128867x","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M128867X","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3159822925.pdf","grobid_xml":"https://content.openalex.org/works/W3159822925.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2064463037"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W4238204885"],"abstract_inverted_index":{"The":[0],"Rodrigues":[1],"formula":[2],"for":[3],"the":[4,33],"3":[5,7],"\\times":[6],"rotation":[8,34],"matrix":[9,35],"is":[10,24,41],"hardly":[11],"ever":[12],"derived":[13],"from":[14],"first":[15],"principles":[16],"in":[17,43],"a":[18,44],"simple":[19,45],"and":[20,46],"intuitive":[21],"way":[22],"that":[23,50],"accessible":[25],"to":[26,57],"undergraduate":[27],"students.":[28],"Two":[29],"different":[30],"derivations":[31],"of":[32],"are":[36],"presented":[37],"here.":[38],"This":[39],"communication":[40],"written":[42],"expository":[47],"style,":[48],"so":[49],"it":[51],"could":[52],"serve":[53],"as":[54],"supplementary":[55],"material":[56],"an":[58],"introductory":[59],"linear":[60],"algebra":[61],"course.":[62]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}