{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,11]],"date-time":"2026-01-11T05:58:21Z","timestamp":1768111101674,"version":"3.49.0"},"reference-count":19,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,4]],"date-time":"2022-08-04T00:00:00Z","timestamp":1659571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001603","name":"Sustainable Energy Authority of Ireland (SEAI)","doi-asserted-by":"publisher","award":["RDD\/00681"],"award-info":[{"award-number":["RDD\/00681"]}],"id":[{"id":"10.13039\/501100001603","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The resolution of the acceleration and jerk vectors of a particle moving on a space curve in the Euclidean 3-space is considered. By applying this resolution and Siacci\u2019s theorem, alternative resolutions of acceleration and jerk vectors are derived based on the quasi-frame. In the osculating plane, the acceleration vector is resolved as the sum of its tangential and radial components. In addition, in the osculating and rectifying planes, the jerk vector is resolved along the tangential direction and two special radial directions. The maximum permissible speed on a space curve at all trajectory points is established via the jerk vector formula. Finally, some examples are presented to illustrate how the results work.<\/jats:p>","DOI":"10.3390\/sym14081610","type":"journal-article","created":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T02:12:39Z","timestamp":1659665559000},"page":"1610","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Motion along a Space Curve with a Quasi-Frame in Euclidean 3-Space: Acceleration and Jerk"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3574-2939","authenticated-orcid":false,"given":"Ahmed M.","family":"Elshenhab","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3850-1022","authenticated-orcid":false,"given":"Osama","family":"Moaaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"}]},{"given":"Ioannis","family":"Dassios","sequence":"additional","affiliation":[{"name":"FRESLIPS, University College Dublin, Dublin D4, Ireland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0288-2548","authenticated-orcid":false,"given":"Ayman","family":"Elsharkawy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31511, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,4]]},"reference":[{"key":"ref_1","first-page":"946","article-title":"Moto per Una Linea Gobba","volume":"14","author":"Siacci","year":"1879","journal-title":"Atti R. Accad. Sci. Torino"},{"key":"ref_2","unstructured":"Whittaker, E.T. (1944). 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