On the relative movement of equivalent reference systems

The purpose of the paper is to establish an equation that determines the common element of continuous symmetry of a noninertial rigid reference frame in the classical case. The basis of the analytical method is the generalized principle of relativity of A. A. Logunov. According to this principle, Lagrangians of equivalent reference systems have the same parameters: proper accelerations and angular velocities. This condition severely limits the breadth of the symmetry transformations and allows us to establish a differential equation for the motion of an equivalent reference system with respect to the original system. The general form of the equations solution depends on the solution of the Darboux problem.