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.
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Acknowledgements
This article is dedicated to the memory of Professor Salvatore Rionero whose research has greatly contributed to the foundation of theoretical models. This work was partially supported by National Group of Mathematical Physics GNFM-INdAM (Italy).
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Gouin, H. Principle of virtual action in continuum mechanics. Ricerche mat 73 (Suppl 1), 217–232 (2024). https://doi.org/10.1007/s11587-023-00785-x
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DOI: https://doi.org/10.1007/s11587-023-00785-x