The variational principle of displacement in dynamics of discrete systems
Zeng Qing-yuan
Abstract
Zeng Qing-yuan
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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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