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1975
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Euler-Lagrange equations Equations, Lagrange D'Alembert equation Equations, Euler-Lagrange Lagrangian equationsCiter ce document
Maurice Anthony Biot, « A virtual dissipation principle and Lagrangian equations in non-linear irreversible thermodynamics », Bulletins de l'Académie Royale de Belgique, ID : 10.3406/barb.1975.57878
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. — A principle of virtual dissipation is derived which genera¬ lizes d'Alembert's principle to non-linear irreversible thermodynamics, leading to a corresponding Hamiltonian form and Lagrangian equations. It constitutes the fundamental mathematical tool for the analysis of general non-linear dissipative physical systems by methods similar to those of classical mechanics. The principle provides a derivation of the differential field equations or the Lagrangian equations which govern any particular dissipative thermodynamic system and is not based on a priori knowledge of the field equations. Results are essentially an ultimate development of the author's earlier work originated in 1954 which was presented in a more restricted context.