The goal of this project is to develop group-theoretical techniques to model, analyze, and fabricate complex systems, with particular emphasis in a Coupled Inertial Navigation Sensor (CINS) system made up of coupled vibratory gyroscopes. Current prototype Micro-Electro-Mechanical Systems gyroscopes are compact and inexpensive to produce but their performance characteristics, in particular drift rate, fail to meet the requirements for an inertial guidance system. The underlying principle of the project is to investigate the conditions for the existence and stability of synchronization states among the sensing modes of each of the individual gyroscopes, which preliminary results suggest that such states can produce better robustness by minimizing phase drift and susceptibility to jamming and other interferences. The approach to be used will exploit the symmetry of the system directly to: formulate appropriate models; analyze the dynamics; outline a systematic procedure for deriving reduced models that can preserve the large-scale features of a CINS system while being amenable to analysis; and be able to predict behavior before the system can be fabricated.
The research objectives outline above will help advance the design and fabrication of complex engineered systems with gyroscopic forces, such as navigational systems, hydroelastic and rotating systems, mono-trains and boats/ships. From a mathematical point of view, the project will help advance the field of bifurcations of coupled mechanical systems with symmetries. From the educational point of view, the project will directly impact the preparation of future computational scientists, engineers, and applied mathematicians. In particular, recruiting and training of underrepresented minorities for careers in science and engineering will be pursued through established channels at the university, which already has a 40% population of students from traditionally underrepresented groups. Outreach activities include exhibits at a local museum and formal presentations at national and international conferences. Additionally, graduate students will participate in summer internships with collaborators from a local Navy laboratory to work on translational research tasks to fabricate the CINS device.
