Principle of virtual action in continuum mechanics

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 e...

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Bibliographic Details
Published in:Ricerche di matematica 2024-01, Vol.73 (Suppl 1), p.217-232
Main Author: Gouin, Henri
Format: Article
Language:English
Subjects:
Algebra
Analysis
Classical mechanics
Complex systems
Continuum mechanics
Engineering Sciences
Geometry
Mathematical Physics
Mathematics
Mathematics and Statistics
Mechanics
Numerical Analysis
Physics
Principles
Probability Theory and Stochastic Processes
Relativity
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Summary: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.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-023-00785-x