On the Various Aspects of Hamiltonian Description of the Mechanics of Continuous Media

Details On the Various Aspects of Hamiltonian Description of the Mechanics of Continuous Media On the Various Aspects of Hamiltonian Description of the Mechanics of Continuous Media

2009-08-21

arxiv.org/abs/0908.3096v1

Physics

Mathematical Physics

40 pages, 1 figure

Scientific paper

We consider a general approach to the theory of continuous media starting from Lagrangian formalism. This formalism which uses the trajectories if constituents of media is very convenient for taking into account different types of interaction between particles typical for different media. Building the Hamiltonian formalism we discuss some issues which is not very well known, such as relation of famous Thompson theorem with the symmetry with respect to volume preserving diffeomorphisms. We also discuss the relation between Euler and Lagrange description and present similar to Euler $C^2$ formulation of continuous mechanics. In these general frameworks we consider as examples the theory of plasma and gravitating gas.

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