Knowing this, the attitude pointing characteristics spectra can be constructed as shown in Figs. 2 through 4, by making a large number of solutions for Eqs. 12 through 16 with various values of /. To visualize the solutions of the system Eq. 5, look at the phase plane in Fig. 4. These curves represent the angle rate 0„/wo plotted against the attitude angle, The area is preserved under the shift along its phase trajectories so that the phase diagram does not contain rest points attracting or repulsing trajectories (i.e., nodal and focal points). The diagram has a periodic structure with a maximum angle = 18.8° occurring with the inertia ratio / = 1 and the angle rate 0y = 0. Note that in this case, every periodic motion is Lyapunov unstable (3). Indeed, with the oscillation period being dependent on the amplitude, every infinitesimal shift of the moving point to a neighboring trajectory results in a finite deviation between the points for infinitely increasing time, t. However, the trajectories of motion of the representing points will remain close to each other all the time, and orbital stability is obtained in such a case.
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