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

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 (x_1e, 0, 0), x_1e ≠ 0, and (0, 0,x_3e), x_3e ≠ 0, are Lyapunov stable while equilibria of the form (0,x_2e, 0), x_2e ≠ 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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