Show that the rigid spacecraft dynamical system in Example 3.1 is at an equilibrium if and only if a

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Show that the rigid spacecraft dynamical system in Example 3.1 is at an equilibrium if and only if at least two of the quantities (x1,x2,x3) are equal to zero, and hence, the set of equilibria consists of the union of the x1, x2, and x3 axes. Furthermore, show that equilibria of the form (x1e, 0, 0), x1e ≠ 0, and (0, 0,x3e), x3e ≠ 0, are Lyapunov stable while equilibria of the form (0,x2e, 0), x2e ≠ 0, are unstable. What does this result imply in regards to the spacecraft spinning about its major, minor, and intermediate axes?

 

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