Abstract

In this paper, recent results regarding generalized continuum mechanics on oriented Riemannian manifolds are reviewed and summarized. The mass, the momentum and the energy conservation laws are given. Thermodynamics arising in such media is also considered as a Lagrangian manifold endowed with a Riemannian structure. Thermodynamic model of moving media takes into account deformation and stress arising in a media in motion.

中文翻译：

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运动介质的动力学和热力学

摘要

本文对定向黎曼流形上广义连续介质力学的最新研究成果进行了回顾和总结。给出了质量、动量和能量守恒定律。在这种介质中产生的热力学也被认为是具有黎曼结构的拉格朗日流形。移动介质的热力学模型考虑了运动介质中产生的变形和应力。