Lagrangian representation of the family of Gordon–Schowalter objective derivatives at simple shear

The paper deals with the one-parameter family of Gordon–Showalter objective derivatives, which includes the Oldroyd, Cotter–Rivlin, and Jaumann derivatives. For a simple shift, movable bases were found in which the considered differential operators are reduced to the total time derivatives of the tensor components. For all derivatives of the family under consideration, except for Oldroyd and Cotter–Rivlin derivatives, the vectors of bases lying in the shear plane rotate with a certain period, changing their length and mutual orientation.