Acceleration Energies and Higher-Order Dynamic Equations in Analytical Mechanics

Iuliu Negrean (), Adina Veronica Crișan () and Sorin Vlase
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Iuliu Negrean: Technical Sciences Academy of Romania, 26 Dacia Boulevard, 030167 Bucharest, Romania
Adina Veronica Crișan: Department of Mechanical Systems Engineering, Technical University of Cluj-Napoca, 103-105 Muncii Bld., 400641 Cluj-Napoca, Romania
Sorin Vlase: Technical Sciences Academy of Romania, 26 Dacia Boulevard, 030167 Bucharest, Romania

Mathematics, 2025, vol. 13, issue 10, 1-29

Abstract: The dynamic study of current and rapid movements of rigid and multibody mechanical systems, according to differential principles from dynamics, is based on advanced concepts from analytical mechanics: kinetic energy, higher-order acceleration energies, and their absolute time derivatives. In advanced dynamics, the study will extend to higher-order acceleration energies. This paper, reflecting the authors’ research, presents new and revised formulations in advanced kinematics and dynamics, with a focus on acceleration energies of the higher order. Explicit and matrix representations of the defining expressions for higher-order acceleration energies, relevant to the current and rapid movements of rigid bodies and multibody mechanical systems, are presented. These formulations include higher-order absolute time derivatives of advanced concepts, following the specific equations from analytical dynamics. Based on the authors’ findings, acceleration energies play a central, decisive role in formulating higher-order differential equations, which describe both rapid and transient motion behavior in rigid and multibody systems.

Keywords: mechanics; analytical dynamics; kinetic energy; acceleration energies; advanced dynamic equations; robotics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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