Fundamental Principles and Laws of Continuum Mechanics
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We derive in this chapter the governing differential equations of continuum mechanics with the aid of the above definitions and the conservation laws for the mass, momentum, energy, and momentum moment written for finite volumes of a continuum. The differential equations of continuum mechanics (equations of continuity, momentum, and energy) represent the partial differential equations written in the Lagrangian and Eulerian coordinates. They are applicable for the description of any continua. The specification of a continuum is achieved by specifying the equation of state. We discuss in the present chapter the general principles of the construction of the equations of state and their form in the simplest case of an ideal and viscous, heat-conducting gas.
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