Outline of Stability Analysis.
Final technical rept. Volume 1,
ALABAMA UNIV HUNTSVILLE RESEARCH INST
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The modified Euler equations are formulated for a gyroscope on gimbal rings mounted on a moving vehicle, the mass and inertial moments of the inner gimbal ring being variable. In a first approximation, the governing differential equations of the system are close in behavior to Hills equation. Some simple models are discussed in detail. In general, no reliable conclusions on the behavior regarding finite time stability and practical stability of the actual system may be drawn from this analysis. A numerical method applicable to a broad class of systems is proposed to obtain directly the stability domain in parameter space as well as numerical bounds for practical stability over a finite time interval. The first step is based on an application of the invariant imbedding approach, the second on integrating the governing differential equation with a random excitation. Author
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