Abstract
Abstract For a class of systems obeying Euler's equation of motion the existence of a quantity to be named "proper mechanical energy" (PME) is shown which, together with internal energy, results in a quantity to be named "proper energy" (PE), which is conserved under conditions of time-dependent potentials. The appertaining formal structure for the continuum mechanics of such systems is the counterpart to Gibbs' fundamental equation of thermodynamics and the relations deriving therefrom. Euler's equation of motion, in particular, corresponds to the Gibbs-Duhem equation of thermodynamics. The transport properties of PME and PE are different from those of the corresponding conventional energies. The results point to a general structure of this kind for continuum mechanics.
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