Abstract:
Xing ZiZheng1, He XiaoKai2, CAO ZhouJian1
(1. School of Physics and Astronomy,Beijing Normal University, Beijing 100875, China; 
2. School of Mathematics and Statistics, Hunan First Normal University, Changsha, Hunan 410205, China)

Abstract:Lagrange theory is an important teaching content in theoretical mechanics and celestial mechanics. The perfect fluid, as a paradigm of field theory, is also an important teaching content in theoretical mechanics, celestial mechanics, and field theory. But interestingly, there are few textbooks that explain fluid mechanics from the perspective of Lagrangian theory. This article combines thermodynamics, generalized coordinate transformation, and differomorphism together to analyze the Lagrangian theory of perfect fluids.  A mathematical theorem which provides a restriction condition for the generalized coordinates of Lagrange theory is specifically discussed. This theorem demonstrates the non-existence of a Lagrangian theory for a perfect fluid with only three field quantities including particle number density, fluid energy density, and four velocity field as generalized coordinates. The content of this article can not only help readers deepen their understanding on thermodynamics in fluid mechanics, differomorphism transformation in general relativity, generalized coordinate transformation in Lagrangian theory, and Lagrangian theory description of fluids, but also help readers further understand Lagrangian theory itself. The contents