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Open AccessArticle

A New Approach in Analytical Dynamics of Mechanical Systems

1
Department of Mechanical Systems Engineering, Faculty of Machine Building, Technical University of Cluj–Napoca, 400641 Cluj–Napoca, Romania
2
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; https://doi.org/10.3390/sym12010095
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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