In the paper, using a linear in angular velocity approximation, two basic well-known systems of Maxwell’s equations in a uniformly rotating frame of reference are considered. The first system of equations was first obtained in the work [L. I. Schiff, Proc. Natl. Acad. Sci. USA 25, 391 (1939)] on the base of use of the formalism of the theory of general relativity, and the second one – in the work [W. M. Irvine, Physica 30, 1160 (1964)] on the base of use of the method of orthonormal tetrad in this theory. In the paper, in the approximation of plane waves, these two vectorial systems of Maxwell’s equations are simplified and rewritten in cylindrical coordinates in scalar component form in order to find the lows of propagation of transversal components of electromagnetic waves in a circular resonator of ring laser gyro in the case of its rotation about sensitivity axis. On the base of these two simplified systems of Maxwell’s equations, the well-known wave equation and its analytical solutions for the named transversal components are obtained. As a result of substitution of these solutions into the first and second simplified systems of Maxwell’s equations, it is revealed that they satisfy only the second one. On this basis, the conclusion is made that the second system of Maxwell’s equations is more suitable for application in the theory of ring laser gyro than the first one.
Two basic systems of maxwell’s equations in a rotating frame: application in theory of ring laser gyro
