Spatial Equilibrium In Deviations PDF Download

No theoretical technique exists yet that enables the engineer to completely determine the stability of practical complex spacecraft attitude control systems. In this dissertation, a stability approach is developed that utilizes a computer simulation in conjunction with theoretical techniques to locate the potentially troublesome regions of state space and explore their acceptability. It is shown in Part I that for general physical systems, x = f(x), all limit cycles are associated with equilibrium points that lie "inside" the limit cycles. Thus, if no equilibrium point exists in a region, then no limit cycle is contained in that region. Special properties of limit cycles and equilibrium points are discussed and illustrated. In Part II, equilibrium points are found analytically for spacecraft attitude control systems. A method is devised to determine stability near these equilibrium points. Then, instead of utilizing a uniform or random n-dimensional grid of computer initial conditions, a grid is concentrated around a few calculated points. Several practical examples of actual systems are presented. When control systems are viewed in this light, a high degree of confidence is gained from far fewer computer runs than previously needed.