【讨论】关于拉格朗日描述和欧拉描述

Linda010

在有限元教程里，两种描述一带而过，很难理解透彻。那位大牛能否讲解一下？

hxong

In fact I think the two different decribe methods are just two different describe WAYS to investigate the same mechanical system phenomenon. From a child we are used to the Lagranre way to describe a mass point,a system or serials of mass points and then to the generalized solids. So in solid mechanics we are used to the Lagranre way. Its kernal is to trace follow a position in a solid system. If we find the displacement function at a certain position(x,y,z) in a solid system of time t and the original position x,y,z, we can say that we have known the whole mechanical system.
But in fluid mechanics this way isn't the most clear and easy way to describe the whole system due to its large flow(deformation). So in nonlinear mechanical system the Eular way is effective. If we find the velocity vector function at a certain position(x,y,z) in a fluid system of time t, then we can say we have known the whole fluid system's mechanical behaviors. In a word, the Eular way not to trace a certain position in the original system but to trace the change of a certain scalar or vector function at some fixed position of the coordinate.

苍山负雪

拉格朗日描述研究的是质点的运动,欧拉描述研究场的变化,两者研究角度不同,但是可以互相转化。流体力学研究一般是基于欧拉描述的，所以参考一些流体力学的教材，里面有清楚的解释。