On Dynamics and Thermodynamics of Moving Media

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.