{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:45:08Z","timestamp":1760240708688,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T00:00:00Z","timestamp":1566864000000},"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>The present paper\u2019s objective is to highlight some new developments of the main author in the field of advanced dynamics of systems and higher order dynamic equations. These equations have been developed on the basis of the matrix exponentials which prove to have undeniable advantages in the matrix study of any complex mechanical system. The present paper proposes some new approaches, based on differential principles from analytical mechanics, by using some important dynamics notions, regarding the acceleration energies of the first, second and third order. This study extended the equations of the higher order, which provide the possibility of applying the initial motion conditions in the positions, velocities and accelerations of the first and second order. In order to determine the time variation laws for the generalized variables, the driving forces and acceleration energies of the higher order are applied by the time polynomial functions of the fifth order. According to inverse kinematics also named control kinematics of the robots, the applications of polynomial functions lead to the kinematic control functions of mechanical motions, especially the transitory motions. They influence the dynamic behavior of multibody systems, in which robot structures are included.<\/jats:p>","DOI":"10.3390\/sym11091077","type":"journal-article","created":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T11:13:30Z","timestamp":1566904410000},"page":"1077","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Synthesis on the Acceleration Energies in the Advanced Mechanics of the Multibody Systems"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0018-5183","authenticated-orcid":false,"given":"Iuliu","family":"Negrean","sequence":"first","affiliation":[{"name":"Faculty of Machine Building, Department of Mechanical Systems Engineering, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4017-9063","authenticated-orcid":false,"given":"Adina-Veronica","family":"Cri\u0219an","sequence":"additional","affiliation":[{"name":"Faculty of Machine Building, Department of Mechanical Systems Engineering, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,27]]},"reference":[{"key":"ref_1","unstructured":"Appell, P. (1899). Sur Une Forme G\u00e9n\u00e9rale des Equations de la Dynamique, Gauthier-Villars. [1st ed.]."},{"key":"ref_2","unstructured":"Appell, P. (1903). Trait\u00e9 de M\u00e9canique Rationnelle, Garnier fr\u00e8res. [1st ed.]."},{"key":"ref_3","unstructured":"Craig, J.J. (2005). Introduction to Robotics: Mechanics and Control, Pearson Prentice Hall. [3rd ed.]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1115\/1.2899115","article-title":"Dynamics of Flexible Manipulator Arms: Alternative derivation, Verification, and Characteristics for Control","volume":"115","author":"Yuan","year":"1993","journal-title":"ASME J. Dyn. Syst. Meas. Control"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Bhatti, M., and Lu, D. (2019). Analytical Study of the Head-On Collision Process between Hydroelastic Solitary Waves in the Presence of a Uniform Current. 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Orientation, Rotation, Velocity and Acceleration, and the SRM, User\u2019s manual, version 2.0; SEDRIS."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/9\/1077\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:14:29Z","timestamp":1760188469000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/9\/1077"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,27]]},"references-count":20,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["sym11091077"],"URL":"https:\/\/doi.org\/10.3390\/sym11091077","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,8,27]]}}}