{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T01:25:52Z","timestamp":1766712352303,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T00:00:00Z","timestamp":1651017600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Multibody mechanical systems (i.e., serial, and parallel robots) have a wide range of applications in the industrial field. In technological processes, these systems perform mechanical movements, in which the active forces have a certain time variation law and, hence, induce higher-order accelerations in the mechanical system, which become central functions in acceleration energies. The advanced dynamics study of multibody systems, often characterized by symmetry, is conducted by applying the differential and variational principles. Lagrange\u2013Euler equations and their time derivatives are commonly used. Here, the central function is the kinetic energy and its higher-order time derivatives. Additionally, the generalization of Gibbs\u2013Appell equations, where the central function is represented by the first and higher-order acceleration energy, can be applied. This paper aims to establish a relation between the kinetic energy and acceleration energy for different material systems. This purpose is achieved by applying the absolute second-order time derivative on the expressions of kinetic energy, corresponding to different material systems. Following this differential calculation and by applying some constraints, the relationship between kinetic energy and acceleration energy is obtained. For validating the relation between kinetic energy and acceleration energy of the first, second and third order, an application is presented.<\/jats:p>","DOI":"10.3390\/sym14050896","type":"journal-article","created":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T22:20:20Z","timestamp":1651098020000},"page":"896","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["New Formulations on Kinetic Energy and Acceleration Energies in Applied Mechanics of Systems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0018-5183","authenticated-orcid":false,"given":"Iuliu","family":"Negrean","sequence":"first","affiliation":[{"name":"Department of Mechanical Systems Engineering, Faculty of Machine Building, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania"},{"name":"Romanian Academy of Technical Sciences, 030167 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4017-9063","authenticated-orcid":false,"given":"Adina","family":"Cri\u0219an","sequence":"additional","affiliation":[{"name":"Department of Mechanical Systems Engineering, Faculty of Machine Building, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0195-5701","authenticated-orcid":false,"given":"Florina","family":"\u0218erdean","sequence":"additional","affiliation":[{"name":"Department of Mechanical Systems Engineering, Faculty of Machine Building, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8679-2579","authenticated-orcid":false,"given":"Sorin","family":"Vlase","sequence":"additional","affiliation":[{"name":"Romanian Academy of Technical Sciences, 030167 Bucharest, Romania"},{"name":"Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transilvania University of Brasov, 500036 Brasov, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1088\/0031-9120\/49\/5\/564","article-title":"History of physical terms: \u2018Energy\u2019","volume":"49","author":"Frontali","year":"2014","journal-title":"Phys. Educ."},{"key":"ref_2","unstructured":"Negrean, I., Duca, A., Negrean, C., and Kacso, K. (2008). Advanced Mechanics in Robotics, UT Press."},{"key":"ref_3","unstructured":"Appell, P. (1903). Trait\u00e9 de M\u00e9canique Rationnelle, Garnier Fr\u00e8res. [1st ed.]."},{"key":"ref_4","unstructured":"Pars, L.A. (2007). A Treatise on Analytical Dynamics, Heinemann."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Jazar, R.N. (2010). Theory of Applied Robotics: Kinematics, Dynamics, and Control, Springer. [2nd ed.].","DOI":"10.1007\/978-1-4419-1750-8"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cassel, K. (2013). Variational Methods with Applications in Science and Engineering, Cambridge University Press.","DOI":"10.1017\/CBO9781139136860"},{"key":"ref_7","unstructured":"Appell, P. (1899). Sur Une Forme G\u00e9n\u00e9rale des Equations de la Dynamique, Gauthier-Villars. 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