A New Approach in Analytical Dynamics of Mechanical Systems

• Main Authors: Iuliu Negrean, Adina-Veronica Crișan, Sorin Vlase
• Format: Article
• Language: English
• Published: MDPI AG 2020-01-01
• Series: Symmetry
• Subjects: advanced mechanics; analytical dynamics; acceleration energies; matrix exponentials
• Online Access: https://www.mdpi.com/2073-8994/12/1/95

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.