I am confused about the use of two-point tensors in elasticity. The deformation tensor F and first PK tensor are two point tensors, and the "two-point" property arises from use of two different Coordinate System When a continuum body is deformed, why it is necessary to move the Coordinate System as well? (or alternatively, why the coordinate system is attached to the body itself??, isn't it possible to use a general coordinate system which can represent the deformations and also account for the rigid body rotations of the continuum body?).
I suppose the sole purpose of using new coordinate system associated with the deformation is to separate the rigid body rotations during the deformation and the new CS provides rotation-free deformations. If my idea is not correct please suggest/reply with some simple
Please note: My question is about the coordinate systems, (not about coordinate values).