Reduction of the excess of natural coordinates in the calculation of crystal lattice vibrations

The simplification of the procedure of setting up the equations of crystal lattice vibrations in terms of dependent natural vibration coordinates by choosing a rational coordinate system and introducing symmetrical linear combinations of coordinates, thus reducing the excess of coordinates, is considered. Vibrations in a plane square lattice are used to illustrate the method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 63–67, September, 1984.