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Open AccessArticle

A New Approach in Analytical Dynamics of Mechanical Systems

Department of Mechanical Systems Engineering, Faculty of Machine Building, Technical University of Cluj–Napoca, 400641 Cluj–Napoca, Romania
Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transilvania University of Brașov, 500036 Brașov, Romania
Authors to whom correspondence should be addressed.
Symmetry 2020, 12(1), 95;
Received: 8 October 2019 / Revised: 19 December 2019 / Accepted: 26 December 2019 / Published: 3 January 2020
(This article belongs to the Special Issue Conservation Laws and Symmetries of Differential Equations)
This paper presents a new approach to the advanced dynamics of mechanical systems. It is known that in the movements corresponding to some mechanical systems (e.g., robots), accelerations of higher order are developed. Higher-order accelerations are an integral part of higher-order acceleration energies. Unlike other research papers devoted to these advanced notions, the main purpose of the paper is to present, in a matrix form, the defining expressions for the acceleration energies of a higher order. Following the differential principle in generalized form (a generalization of the Lagrange–D’Alembert principle), the equations of the dynamics of fast-moving systems include, instead of kinetic energies, the acceleration energies of higher-order. To establish the equations which characterize both the energies of accelerations and the advanced dynamics, the following input parameters are considered: matrix exponentials and higher-order differential matrices. An application of a 5 d.o.f robot structure is presented in the final part of the paper. This is used to illustrate the validity of the presented mathematical formulations. View Full-Text
Keywords: advanced mechanics; analytical dynamics; acceleration energies; matrix exponentials advanced mechanics; analytical dynamics; acceleration energies; matrix exponentials
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Negrean, I.; Crișan, A.-V.; Vlase, S. A New Approach in Analytical Dynamics of Mechanical Systems. Symmetry 2020, 12, 95.

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