A New Approach in Analytical Dynamics of Mechanical Systems
| Autor: | Sorin Vlase, Adina-Veronica Crişan, Iuliu Negrean |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics and Astronomy (miscellaneous)
Generalization Computer science General Mathematics Structure (category theory) matrix exponentials 02 engineering and technology 01 natural sciences Matrix (mathematics) Acceleration 0203 mechanical engineering Computer Science (miscellaneous) Applied mathematics 0101 mathematics Differential (infinitesimal) lcsh:Mathematics advanced mechanics lcsh:QA1-939 Analytical dynamics Exponential function 010101 applied mathematics Mechanical system acceleration energies 020303 mechanical engineering & transports analytical dynamics Chemistry (miscellaneous) |
| Zdroj: | Symmetry Volume 12 Issue 1 Symmetry, Vol 12, Iss 1, p 95 (2020) |
| ISSN: | 2073-8994 |
| DOI: | 10.3390/sym12010095 |
| Popis: | 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&ndash 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. |
| Databáze: | OpenAIRE |
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