{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T06:57:29Z","timestamp":1719989849447},"reference-count":43,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1016\/j.cam.2022.114766","type":"journal-article","created":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T13:55:27Z","timestamp":1661435727000},"page":"114766","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Non-parabolic conical rotations"],"prefix":"10.1016","volume":"420","author":[{"given":"H. Bar\u0131\u015f","family":"\u00c7olako\u011flu","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5674-8219","authenticated-orcid":false,"given":"\u0130skender","family":"\u00d6zt\u00fcrk","sequence":"additional","affiliation":[]},{"given":"Mustafa","family":"\u00d6zdemir","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"01","key":"10.1016\/j.cam.2022.114766_b1","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1501\/Commua1_0000000312","article-title":"On the rotation matrices in the semi-Euclidean space","volume":"55","author":"B\u00fckc\u00fc","year":"2006","journal-title":"Commun. Fac. Sci. Univ. Ankara Ser. A1 Math. Stat."},{"issue":"1","key":"10.1016\/j.cam.2022.114766_b2","doi-asserted-by":"crossref","first-page":"11","DOI":"10.36753\/mathenot.642208","article-title":"Simple, double and isoclinic rotations with a viable algorithm","volume":"8","author":"Erdo\u011fdu","year":"2020","journal-title":"Math. Sci. Appl. E-Notes"},{"issue":"1","key":"10.1016\/j.cam.2022.114766_b3","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/S0034-4877(14)60055-0","article-title":"On the rotation matrix in Minkowski space-time","volume":"74","author":"\u00d6zdemir","year":"2014","journal-title":"Rep. Math. Phys."},{"key":"10.1016\/j.cam.2022.114766_b4","series-title":"Complex Numbers in Geometry","author":"Yaglom","year":"2014"},{"issue":"1","key":"10.1016\/j.cam.2022.114766_b5","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1068\/b050089","article-title":"On the three types of complex number and planar transformations","volume":"5","author":"Rooney","year":"1978","journal-title":"Environ. Plan. B: Plann. Des."},{"key":"10.1016\/j.cam.2022.114766_b6","series-title":"Advances on Theory and Practice of Robots and Manipulators","first-page":"55","article-title":"Generalised complex numbers in mechanics","author":"Rooney","year":"2014"},{"issue":"4","key":"10.1016\/j.cam.2022.114766_b7","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1080\/07468342.1995.11973712","article-title":"The hyperbolic number plane","volume":"26","author":"Sobczyk","year":"1995","journal-title":"College Math. J."},{"issue":"4","key":"10.1016\/j.cam.2022.114766_b8","doi-asserted-by":"crossref","first-page":"377","DOI":"10.5951\/MT.61.4.0377","article-title":"Gaussian, parabolic, and hyperbolic numbers","volume":"61","author":"Miller","year":"1968","journal-title":"Math. Teach."},{"key":"10.1016\/j.cam.2022.114766_b9","series-title":"Geometry of Mobius Transformations: Elliptic, Parabolic and Hyperbolic Actions of SL2(R)","author":"Kisil","year":"2012"},{"issue":"2","key":"10.1016\/j.cam.2022.114766_b10","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1080\/0025570X.2004.11953236","article-title":"Geometry of generalized complex numbers","volume":"77","author":"Harkin","year":"2004","journal-title":"Math. Mag."},{"key":"10.1016\/j.cam.2022.114766_b11","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.laa.2016.01.038","article-title":"Generating hyperbolical rotation matrix for a given hyperboloid","volume":"496","author":"Simsek","year":"2016","journal-title":"Linear Algebra Appl."},{"issue":"5","key":"10.1016\/j.cam.2022.114766_b12","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1119\/1.14605","article-title":"Extending special relativity via the perplex numbers","volume":"54","author":"Fjelstad","year":"1986","journal-title":"Amer. J. Phys."},{"issue":"1","key":"10.1016\/j.cam.2022.114766_b13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00006-018-0833-3","article-title":"Introduction to hybrid numbers","volume":"28","author":"\u00d6zdemir","year":"2018","journal-title":"Adv. Appl. Clifford Algebras"},{"issue":"3\u20134","key":"10.1016\/j.cam.2022.114766_b14","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.physletb.2005.08.072","article-title":"Relativistic quantum physics with hyperbolic numbers","volume":"625","author":"Ulrych","year":"2005","journal-title":"Phys. Lett. B"},{"key":"10.1016\/j.cam.2022.114766_b15","series-title":"The Mathematics of Minkowski Space-Time: with an Introduction to Commutative Hypercomplex Numbers","author":"Catoni","year":"2008"},{"issue":"5","key":"10.1016\/j.cam.2022.114766_b16","first-page":"475","article-title":"Hyperbolic trigonometry in two-dimensional space-time geometry","volume":"118","author":"Catoni","year":"2003","journal-title":"Nuovo Cimento B Serie"},{"issue":"4","key":"10.1016\/j.cam.2022.114766_b17","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1007\/s00006-015-0530-4","article-title":"One-parameter planar motions in generalized complex number plane","volume":"25","author":"Gurses","year":"2015","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"10.1016\/j.cam.2022.114766_b18","series-title":"Geometric Methods and Applications: For Computer Science and Engineering, Vol. 38","author":"Gallier","year":"2011"},{"key":"10.1016\/j.cam.2022.114766_b19","series-title":"Quaternions and Rotations in 3-Space: the Algebra and Its Geometric Interpretation","author":"Vicci","year":"2001"},{"issue":"3","key":"10.1016\/j.cam.2022.114766_b20","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1145\/195784.197480","article-title":"Visualizing quaternion rotation","volume":"13","author":"Hart","year":"1994","journal-title":"ACM Trans. Graph."},{"key":"10.1016\/j.cam.2022.114766_b21","series-title":"Vmv, Vol. 1","first-page":"399","article-title":"Using quaternions for parametrizing 3-D rotations in unconstrained nonlinear optimization","author":"Schmidt","year":"2001"},{"issue":"2","key":"10.1016\/j.cam.2022.114766_b22","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.geomphys.2005.02.004","article-title":"Rotations with unit timelike quaternions in Minkowski 3-space","volume":"56","author":"\u00d6zdemir","year":"2006","journal-title":"J. Geom. Phys."},{"key":"10.1016\/j.cam.2022.114766_b23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.7546\/jgsp-39-2015-1-16","article-title":"On reflections and rotations in Minkowski 3-space of physical phenomena","volume":"39","author":"Erdo\u011fdu","year":"2015","journal-title":"J. Geom. Symmetry Phys."},{"issue":"6","key":"10.1016\/j.cam.2022.114766_b24","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.4134\/JKMS.2007.44.6.1313","article-title":"Split quaternions and rotations in semi Euclidean space E24","volume":"44","author":"Kula","year":"2007","journal-title":"J. Korean Math. Soc."},{"issue":"1","key":"10.1016\/j.cam.2022.114766_b25","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s00006-015-0601-6","article-title":"On rotation about lightlike axis in three-dimensional Minkowski space","volume":"26","author":"Ne\u0161ovi\u0107","year":"2016","journal-title":"Adv. Appl. Clifford Algebras"},{"issue":"1","key":"10.1016\/j.cam.2022.114766_b26","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s00006-015-0592-3","article-title":"An alternative approach to elliptical motion","volume":"26","author":"\u00d6zdemir","year":"2016","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"10.1016\/j.cam.2022.114766_b27","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.laa.2003.07.009","article-title":"G-reflectors: Analogues of Householder transformations in scalar product spaces","volume":"385","author":"Mackey","year":"2004","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"10.1016\/j.cam.2022.114766_b28","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1137\/040619363","article-title":"Structured factorizations in scalar product spaces","volume":"27","author":"Mackey","year":"2005","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"10.1016\/j.cam.2022.114766_b29","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1137\/0118002","article-title":"On isometries of generalized inner product spaces","volume":"18","author":"R\u00e4tz","year":"1970","journal-title":"SIAM J. Appl. Math."},{"issue":"5","key":"10.1016\/j.cam.2022.114766_b30","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1016\/j.laa.2010.11.005","article-title":"An algorithm for the Cartan\u2013Dieudonn\u00e9 theorem on generalized scalar product spaces","volume":"434","author":"Rodr\u00edguez-Andrade","year":"2011","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.cam.2022.114766_b31","series-title":"Affine Maps, Euclidean Motions and Quadrics","author":"Tarrida","year":"2011"},{"key":"10.1016\/j.cam.2022.114766_b32","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/S0024-3795(01)00296-8","article-title":"Constructive ways for generating (generalized) real orthogonal matrices as products of (generalized) symmetries","volume":"332","author":"Uhlig","year":"2001","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"10.1016\/j.cam.2022.114766_b33","doi-asserted-by":"crossref","first-page":"319","DOI":"10.3906\/mat-1904-56","article-title":"A generalization of the Minkowski distance and new definitions of the central conics","volume":"44","author":"\u00c7\u011flu","year":"2020","journal-title":"Turkish J. Math."},{"issue":"1\u20133","key":"10.1016\/j.cam.2022.114766_b34","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/S0024-3795(01)00598-5","article-title":"Symmetric matrices with respect to sesquilinear forms","volume":"349","author":"Mehl","year":"2002","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"10.1016\/j.cam.2022.114766_b35","first-page":"10","article-title":"Computing exponentials of skew-symmetric matrices and logarithms of orthogonal matrices","volume":"18","author":"Gallier","year":"2003","journal-title":"Int. J. Robot. Autom."},{"issue":"4","key":"10.1016\/j.cam.2022.114766_b36","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1023\/A:1021960405660","article-title":"A formula for the exponential of a real skew-symmetric matrix of order 4","volume":"41","author":"Politi","year":"2001","journal-title":"BIT Numer. Math."},{"issue":"1","key":"10.1016\/j.cam.2022.114766_b37","first-page":"99","article-title":"Formulas for the exponential of a semi skew-symmetric matrix of order 4","volume":"10","author":"Kula","year":"2005","journal-title":"Math. Comput. Appl."},{"key":"10.1016\/j.cam.2022.114766_b38","series-title":"Remarks on the Cayley representation of orthogonal matrices and on perturbing the diagonal of a matrix to make it invertible","author":"Gallier","year":"2006"},{"key":"10.1016\/j.cam.2022.114766_b39","series-title":"Sur Quelques Propri\u00e9t\u00e9s Des D\u00e9terminants Gauches","author":"Cayley","year":"1846"},{"issue":"2","key":"10.1016\/j.cam.2022.114766_b40","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/s00006-009-0148-5","article-title":"Cayley formula, Euler parameters and rotations in 3-dimensional Lorentzian space","volume":"20","author":"\u00d6zkald\u0131","year":"2010","journal-title":"Adv. Appl. Clifford Algebras"},{"issue":"05","key":"10.1016\/j.cam.2022.114766_b41","doi-asserted-by":"crossref","DOI":"10.1142\/S0219887815500589","article-title":"Cayley formula in Minkowski space-time","volume":"12","author":"Erdo\u011fdu","year":"2015","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"issue":"6","key":"10.1016\/j.cam.2022.114766_b42","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1177\/1081286507077982","article-title":"Euler-Rodrigues and Cayley formulae for rotation of elasticity tensors","volume":"13","author":"Norris","year":"2008","journal-title":"Math. Mech. Solids"},{"key":"10.1016\/j.cam.2022.114766_b43","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.laa.2014.05.013","article-title":"M\u00f6bius transformations of matrix polynomials","volume":"470","author":"Mackey","year":"2015","journal-title":"Linear Algebra Appl."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042722003880?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042722003880?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,4,15]],"date-time":"2024-04-15T20:04:27Z","timestamp":1713211467000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042722003880"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3]]},"references-count":43,"alternative-id":["S0377042722003880"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2022.114766","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2023,3]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Non-parabolic conical rotations","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2022.114766","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2022 Elsevier B.V. All rights reserved.","name":"copyright","label":"Copyright"}],"article-number":"114766"}}