2007Journal of Railway Science and EngineeringRequires access

The variational principle of displacement in dynamics of discrete systems

Zeng Qing-yuan

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Abstract

The displacement,work,potential energy,virtual displacement and virtual work were discussed.The instantaneous potential energy was defined through the operation of variational integrals.Then,the variational principle of displacement was derived from d'Alembert-Lagrange principle using the variational integral method.This principle is the development of principle of stationary of potential energy in dynamics,and is also the extension of d'Alembert-Lagrange principle.It simplifies problems of dynamics,and has general application.

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What this paper is about

The displacement,work,potential energy,virtual displacement and virtual work were discussed.The instantaneous potential energy was defined through the operation of variational integrals.Then,the variational principle of displacement was derived from d'Alembert-Lagrange principle using the variational integral method.This principle is the development of principle of stationary of potential energy in dynamics,and is also the extension of d'Alembert-Lagrange principle.It simplifies problems of dynamics,and has general application.

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Available abstract

The displacement,work,potential energy,virtual displacement and virtual work were discussed.The instantaneous potential energy was defined through the operation of variational integrals.Then,the variational principle of displacement was derived from d'Alembert-Lagrange principle using the variational integral method.This principle is the development of principle of stationary of potential energy in dynamics,and is also the extension of d'Alembert-Lagrange principle.It simplifies problems of dynamics,and has general application.

Key concepts: Variational principle, Virtual work, Free energy principle, Displacement (psychology), Hamilton's principle, Work (physics), Luke's variational principle, Variational integrator

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