Torus Bifurcation in Uni-Directional Coupled Gyroscopes

Nowadays, the global positioning system (GPS) is popularly used by the U.S. Navy in navigation systems to gain precise position, velocity, and time information. One of the biggest issues for using GPS is its susceptibility to jamming and other inferences. The received GPS signal is approximately 20 dB below the thermal noise level from a distance 11,000 miles away. Because of these weakness and vulnerability, many other alternative navigation methods are needed to improve performance and reduce the dependency on GPS. One of the main alternative methods is the Inertial Guidance System (IGS) that can operate wherever GPS signals are jammed or denied. A prototypical IGS is composed of three accelerometers to measure linear movement and three angular rate sensors (gyroscopes) to gauge the rotational movement. The main benefit of IGS is its low cost relatively to other methods. Current MEMS (Micro-Electro-Mechanical Systems) gyroscopes are compact and inexpensive, but their performance does not meet the requirements for an inertial grade guidance system. In this work, a difference approach was examined on the dynamics of coupled gyroscopes to improve performance through synchronization referred as vibratory coupled gyroscopes with drive amplitudes' coupling. One of the main discoveries from the coupled gyroscopes' mathematical model is a Torus bifurcation, which leads to synchronized behavior in and array of three gyroscopes uni-directionally coupled.