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Acceleration Energies and Higher-Order Dynamic Equations in Analytical Mechanics

Author

Listed:
  • Iuliu Negrean

    (Technical Sciences Academy of Romania, 26 Dacia Boulevard, 030167 Bucharest, Romania
    Department of Mechanical Systems Engineering, Technical University of Cluj-Napoca, 103-105 Muncii Bld., 400641 Cluj-Napoca, 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
    Department of Mechanical Engineering, Transylvania University of Brasov, 500036 Brasov, Romania)

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.

Suggested Citation

  • Iuliu Negrean & Adina Veronica Crișan & Sorin Vlase, 2025. "Acceleration Energies and Higher-Order Dynamic Equations in Analytical Mechanics," Mathematics, MDPI, vol. 13(10), pages 1-29, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1644-:d:1658133
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