An analytical mechanics approach to the first law of thermodynamics and construction of a variational hierarchy
Abstrak
A simple procedure is presented for the study of 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.
Topik & Kata Kunci
Penulis (1)
Said Hamid
Akses Cepat
- Tahun Terbit
- 2021
- Sumber Database
- DOAJ
- DOI
- 10.2298/TAM200315011S
- Akses
- Open Access ✓