This is in continuation/related to the following question asked in the below link
According to my understanding Lagrangian approach is an approach where you track the individual object of which you want to take measurement of for eg in a fluid flow you track a particular fluid particle and measure the physical quantity of that particular fluid particle.(leading to pathlines)
But in the Eulerian Approach, you basically try to measure the physical properties around a particular area/surface.
In application to continuum mechanics in structure, it is mentioned that the initial/reference position of a body is called as the Lagrangian Configuration and the current position(Mapped from Initial Configuration) is called as Eulerian Approach.
Q1) I am not able to understand why is that so? Is it because of the fact the in Lagrangian Configuration/Initial Condition the body is supposed to be rigid and it becomes easier to understand rigid body motion and when there is no rigid body motion ie when deformation starts to occur we shift to Eulerian Approach to study deformation?
Q2) If the answer to the above question is yes, why is the Eulerian approach used to study deformation and if not why do we use two approaches??
Thanks for your reply. I have been using this particular reference. http://web.mit.edu/abeyaratne/Volumes/RCA_Vol_II.pdf in which Eulerian and Lagrangian configurations are explained.(Page 6, 1.3). Here it describes Eulerian configuration as
"the representation (1.6) which deals with the positions of the particles in the deformed configuration, (the configuration in which the physical quantity is being characterized,) is called the Eulerian or spatial description."
and for lagrangian
"If a reference configuration has been introduced we can label a particle by its position x = χref(p) in that configuration, and this, in turn, allows us to describe physical quantities in Lagrangian form."
This is why I am getting confused with Eulerian and Lagrangian. Is there any specific reason so as to why its named like that?
Adding on more reference for the same with the same query(Why are these configurations called Eulerian or Lagrangian ? )