Abstract
This paper discusses the properties of a periodically dithered-ring-laser gyroscope in the approximation of a single phase-locking equation. We discuss both modulation of the input rotation, the phase of the backscattering, and its amplitude. The first two are found to be mathematically equivalent, and the last case is found to offer no advantages as compared with the undithered case. These conclusions are supported by a heuristic argument. The detailed mathematical treatment is based on Floquet theory, which allows us to obtain results by integrating over one dither period only. The locking condition can be determined from the Floquet exponent. For large input parameters the integration of the differential equation for the Floquet problem becomes numerically overwhelming, and the equivalent formulation in terms of an infinite matrix is utilized. This is evaluated using a method based on matrix continued fractions. In this way no restrictions on the parameters are necessary. The method is applied to the single-frequency dithering, and it is confirmed that the locking at zero rotation rate can be completely eliminated. The calculations also confirm the existence of higher-order lock-in zones, which are large just in those conditions which are optimal near zero rotation rate. Thus we conclude that with sinusoidal dither of one frequency it is not possible to avoid nonlinearities in the gyroscope response. In forthcoming publications we intend to discuss possible schemes to overcome this difficulty.
Published Version
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