Changing the Observer and Moving Materials in Continuum Physics

Objectivity and Frame-Indifference

Abstract

Because one has to distinguish between changing the observer and changing the motion of a material with respect to a standard frame of reference, objectivity and material frame indifference are of different kind and have to be redefined. Besides objectivity and observer invariance of the balance and constitutive equations, the concept of standard frame dependence is introduced. The objectivity of time derivative operators is investigated with the result that the material time derivative is observer-independent. Although objective constitutive properties are standard frame dependent in general, representation theorems, and therefore the reduced forms of the constitutive equations remain still valid. A remark on non-objective force densities and inertial systems is made.