Third-Order Differential Variational Principles and Differential Equations of Motion for Mechanico-Electrical Systems
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Xiangwu Zhang, Naiping Wei, Yuanyuan Li, Xiaoxia Zhao, Wenfeng Luo
This paper investigates the third-order differential variational principles of mechanico-electrical systems and the third-order differential equations of motion for holonomic mechanico-electrical systems. Based on Newton’s laws of motion of mechanical systems and Kirchhoff’s voltage laws of circuit systems, the third-order d’Alembert principles of mechanico-electrical systems are proposed, the third-order d’Alembert-Lagrange principle of mechanico-electrical systems is established and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the several different forms of the third-order differential equations of motion for holonomic mechanico-electrical systems are obtained.
Mechanico-Electrical System; Third-Order D’Alembert Principle; Third-Order D’Alembert-Lagrange Principle; Third-Order Differential Equations of Motion