Аннотация:Various representations of the equations of motion, the heat influx, the
constitutive relations of physical and heat content are given for the new body domain
parametrization. The definition of the kth order moment of a certain quantity with
respect to an orthonormal polynomial systems is given. The expressions of moments
of first- and second-order partial derivatives of a certain tensor field are obtained and
this is also done for some important expressions required for constructing different
variants of the thin body theory.