Lagrangian and eulerian descriptions of phenomena

[fisico30]

lagrangian and eulerian descriptions of phenomena...

hello everyone,

some differential equations are written in terms of a field perspective, some from the point of view of a particle moving through the field...
Navier-stokes eqns can be derived from Newton' s 2nd law applied to a particle.

What advantage is there in viewing things from a particle point of view( Lagrangian view)?
I guess classica mechanics is based on this view.

 

[Andy Resnick]

The two viewpoints are equivalent, but some problems are easier to write down in one particular choice of coordinates. For example, if you want to describe the flow of fluid through a channel, IIRC the Lagrangian viewpoint means you pick a control volume dV and watch the fluid flow through it (i.e. stand on the river bank and watch a static point in space), while the Eulerian view means you choose a fluid element dv and watch it deform over time (i.e. follow a material point in time).

In continuum mechanics, especially fluid mechanics, the Eulerian description is preferred because it's a more natural way to describe how deformation and flow carry momentum and energy, by using the total derivative D/Dt =$\frac{\partial}{\partial t} + v\bullet \nabla$.

 

[Heirot]

Isn't it the other way around? Euler stays put, while Lagrange moves around with the particle?

 

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[Andy Resnick]

Isn't it the other way around? Euler stays put, while Lagrange moves around with the particle?

It could be- I always forget which is which :)