An Analytical Mechanics Approach to the First Law of Thermodynamics and Construction of a Variational Hierarchy

Hamid A Said

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arXiv · 1908.03062

An Analytical Mechanics Approach to the First Law of Thermodynamics and Construction of a Variational Hierarchy

Hamid A Said

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Abstract

A simple procedure is presented to study the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically, a second order quasi-linear wave equation. An immediate implication of this procedure is the formation of a least action principle for the balance of energy with dissipation. The corresponding action functional enables us to establish a complete analytic mechanics for thermomechanical systems: a Lagrangian-Hamiltonian theory, integrals of motion, bracket formalism, and Noether's theorem. Furthermore, we apply our procedure iteratively and produce an infinite sequence of interlocked variational principles, a variational hierarchy, where at each level or iteration the full implication of the least action principle can be shown again.

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Hamid A Said. 2019-08-06. An Analytical Mechanics Approach to the First Law of Thermodynamics and Construction of a Variational Hierarchy. https://arxiv.org/abs/1908.03062

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