{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:45:19Z","timestamp":1760060719918,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T00:00:00Z","timestamp":1758240000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science, Innovations and Technological Development of Serbia","award":["451-03-137\/2025-03\/200251","451-03-137\/2025-03\/200102","IMP-003"],"award-info":[{"award-number":["451-03-137\/2025-03\/200251","451-03-137\/2025-03\/200102","IMP-003"]}]},{"name":"Faculty of Teacher Education, Leposavi\u0107","award":["451-03-137\/2025-03\/200251","451-03-137\/2025-03\/200102","IMP-003"],"award-info":[{"award-number":["451-03-137\/2025-03\/200251","451-03-137\/2025-03\/200102","IMP-003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>In this research, we present the analogies between variational calculations in cosmology and in classical mechanics. Our approach is based on the invariants for transformations of affine connections defined on N-dimensional manifolds (special cases are the 8-dimensional, 5-dimensional, and 4-dimensional manifolds used in cosmology and 2-dimensional manifolds used in classical mechanics). Any of these transformations represents a class of curves on initial manifolds, which transmits to an another class of curves on the current manifolds. The main results of this paper are general equations of motion, which are obtained from the invariants caused by the transformation rule of an initial affine connection to the current one and the corresponding Navier\u2013Stokes equations, recognized in transformations of curves along which moves a fluid particle.<\/jats:p>","DOI":"10.3390\/computation13090226","type":"journal-article","created":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T10:08:58Z","timestamp":1758276538000},"page":"226","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Equations of Motion and Navier\u2013Stokes Equations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1709-0765","authenticated-orcid":false,"given":"Du\u0161an J.","family":"Simjanovi\u0107","sequence":"first","affiliation":[{"name":"Faculty of Information Technology, Belgrade Metropolitan University, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9414-0711","authenticated-orcid":false,"given":"Ivana","family":"Djuri\u0161i\u0107","sequence":"additional","affiliation":[{"name":"Institute for Multidisciplinary Research, University of Belgrade, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0898-6818","authenticated-orcid":false,"given":"Aleksandra","family":"Penji\u0161evi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Economics, Union\u2014Nikola Tesla University, 11000 Belgrade, Serbia"}]},{"given":"Marko","family":"Stefanovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Belgrade Metropolitan University, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0643-0955","authenticated-orcid":false,"given":"Branislav M.","family":"Randjelovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Electronic Engineering, University of Ni\u0161, Aleksandra Medvedeva 14, 18000 Ni\u0161, Serbia"},{"name":"Faculty of Teachers Education, University of K. Mitrovica, 38218 Leposavi\u0107, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,19]]},"reference":[{"key":"ref_1","unstructured":"Dodelson, S. (2003). Modern Cosmology, Elsevier. [1st ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1088\/0143-0807\/29\/4\/011","article-title":"Potential motion in a geometric setting: Presenting differential geometry methods in a classical mechanics course","volume":"29","author":"Deriglazov","year":"2008","journal-title":"Eur. J. Phys."},{"key":"ref_3","unstructured":"Mikes, J., Stepanova, E., Van\u017eurov\u00e1, A., B\u00e1cs\u00f3, S., Berezovski, V.E., Chepurna, O., Formella, S., Gavrilchenko, M.L., Haddad, M., and Hinterleitner, I. (2015). Differential Geometry of Special Mappings, Olomouc University. 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