{"id":"https://openalex.org/W4410864797","doi":"https://doi.org/10.3390/sym17060845","title":"Elliptic and Hyperbolic Rotational Motions on General Hyperboloids","display_name":"Elliptic and Hyperbolic Rotational Motions on General Hyperboloids","publication_year":2025,"publication_date":"2025-05-28","ids":{"openalex":"https://openalex.org/W4410864797","doi":"https://doi.org/10.3390/sym17060845"},"language":"en","primary_location":{"id":"doi:10.3390/sym17060845","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17060845","pdf_url":"https://www.mdpi.com/2073-8994/17/6/845/pdf?version=1748445415","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/6/845/pdf?version=1748445415","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058711752","display_name":"Harun Bar\u0131\u0219 \u00c7olako\u011flu","orcid":"https://orcid.org/0000-0001-5559-9768"},"institutions":[{"id":"https://openalex.org/I197907453","display_name":"Akdeniz University","ror":"https://ror.org/01m59r132","country_code":"TR","type":"education","lineage":["https://openalex.org/I197907453"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Harun Bar\u0131\u015f \u00c7olako\u011flu","raw_affiliation_strings":["Department of Computer Technologies, Akdeniz University, 07070 Antalya, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0001-5559-9768","affiliations":[{"raw_affiliation_string":"Department of Computer Technologies, Akdeniz University, 07070 Antalya, T\u00fcrkiye","institution_ids":["https://openalex.org/I197907453"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092913371","display_name":"Mehmet Duru","orcid":"https://orcid.org/0009-0001-5827-4333"},"institutions":[{"id":"https://openalex.org/I197907453","display_name":"Akdeniz University","ror":"https://ror.org/01m59r132","country_code":"TR","type":"education","lineage":["https://openalex.org/I197907453"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Mehmet Duru","raw_affiliation_strings":["Department of Mathematics, Akdeniz University, 07070 Antalya, T\u00fcrkiye"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Akdeniz University, 07070 Antalya, T\u00fcrkiye","institution_ids":["https://openalex.org/I197907453"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5092913371"],"corresponding_institution_ids":["https://openalex.org/I197907453"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.4838,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.85050269,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"6","first_page":"845","last_page":"845"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.991100013256073,"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/T12504","display_name":"Mathematics and Applications","score":0.991100013256073,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/rotation","display_name":"Rotation (mathematics)","score":0.4936867654323578},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4881930947303772},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4405773878097534},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.388729065656662},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.34945014119148254}],"concepts":[{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.4936867654323578},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4881930947303772},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4405773878097534},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.388729065656662},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.34945014119148254}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17060845","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17060845","pdf_url":"https://www.mdpi.com/2073-8994/17/6/845/pdf?version=1748445415","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17060845","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17060845","pdf_url":"https://www.mdpi.com/2073-8994/17/6/845/pdf?version=1748445415","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410864797.pdf","grobid_xml":"https://content.openalex.org/works/W4410864797.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1622053842","https://openalex.org/W1638721624","https://openalex.org/W1964991686","https://openalex.org/W1973681578","https://openalex.org/W1977369603","https://openalex.org/W2060837274","https://openalex.org/W2078397225","https://openalex.org/W2095234512","https://openalex.org/W2110773940","https://openalex.org/W2126622293","https://openalex.org/W2254513848","https://openalex.org/W2286490889","https://openalex.org/W2322633222","https://openalex.org/W2790485597","https://openalex.org/W2963864828","https://openalex.org/W2963972492","https://openalex.org/W4288935732","https://openalex.org/W4293051488","https://openalex.org/W4297833479","https://openalex.org/W4321187273","https://openalex.org/W4367052779","https://openalex.org/W4386912875","https://openalex.org/W4388103471","https://openalex.org/W4399087023","https://openalex.org/W6679230467"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W2271181815"],"abstract_inverted_index":{"This":[0],"study":[1,51],"proposes":[2],"a":[3,46],"new":[4],"way":[5],"to":[6],"represent":[7],"elliptic":[8,96],"and":[9,26,97],"hyperbolic":[10,98],"motions":[11,86,99],"on":[12,87,100],"any":[13],"general":[14,101],"hyperboloids":[15,102],"of":[16,69,113],"one":[17],"or":[18],"two":[19],"sheets":[20],"using":[21],"the":[22,34,40,57,67,88,114],"famous":[23],"Rodrigues,":[24],"Cayley,":[25],"Householder":[27],"transformations.":[28],"These":[29],"transformations":[30],"are":[31],"used":[32],"within":[33],"generalized":[35,47,63,71],"Minkowski":[36,91],"3-space":[37,92],"which":[38],"extends":[39],"usual":[41],"Lorentzian":[42,72],"geometry":[43],"by":[44,55],"introducing":[45],"scalar":[48],"product.":[49],"The":[50,81],"is":[52,109],"carried":[53],"out":[54],"considering":[56],"unit":[58],"sphere":[59,89],"defined":[60],"in":[61,90,103],"this":[62],"space":[64],"along":[65],"with":[66],"use":[68],"three-dimensional":[70],"skew-symmetric":[73],"matrices":[74],"that":[75],"naturally":[76],"generate":[77],"continuous":[78],"rotational":[79,85],"motions.":[80],"obtained":[82],"results":[83],"provide":[84],"as":[93,95],"well":[94],"Euclidean":[104],"3-space.":[105],"A":[106],"numerical":[107],"example":[108],"provided":[110],"for":[111],"each":[112],"explored":[115],"rotation":[116],"methods.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}