Acceleration Energies and Higher-Order Dynamic Equations in Analytical Mechanics
Iuliu Negrean (),
Adina Veronica Crișan () and
Sorin Vlase
Additional contact information
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
References: Add references at CitEc
Citations:
Downloads: (external link)
https://www.mdpi.com/2227-7390/13/10/1644/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/10/1644/ (text/html)
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:10:p:1644-:d:1658133
Access Statistics for this article
Mathematics is currently edited by Ms. Emma He
More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().