Principle of virtual action in continuum mechanics

Abstract

We present the principle of virtual action as a foundation of continuum mechanics. Used mainly in relativity, the method has a useful application in classical mechanics and places the notion of action as the basic concept of dynamics. The principle is an extension of virtual work to space-time. It extends the efforts made by d'Alembert and Lagrange. Unlike the classical case of equilibrium, the principle of virtual action becomes a postulate for the formulation of models in dynamics. It allows to use a minimal set of clear conjectures and is extended to the case of media with dissipation; it can be used for more complex systems.

References in corpus (4)

• A new form of governing equations of fluids arising from Hamilton's principle
• Symmetric form for the hyperbolic-parabolic system of fourth-gradient fluid model
• Rankine--Hugoniot conditions for fluids whose energy depends on space and time derivatives of density
• Rankine-Hugoniot conditions obtained by using the space-time Hamilton action