连续介质力学哈密顿描述的若干问题
On the Various Aspects of Hamiltonian Description of the Mechanics of Continuous Media
摘要：
我们考虑一个一般的方法从拉格朗日形式主义的连续介质理论。这种形式主义，它使用的轨迹，如果成分的媒体是非常方便的考虑到不同类型的粒子之间的相互作用，典型的不同介质。在建立Hamilton形式体系的基础上，讨论了一些不太为人所知的问题，如著名的Thompson定理与保体积超同态的对称性之间的关系。讨论了欧拉描述与拉格朗日描述之间的关系，给出了连续力学中类似欧拉描述的$C^2$列式。在这些一般框架中，我们考虑等离子体理论和引力气体作为例子。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
