(a) Using the notation and initial conditions of the example in Section 8.7.6, prove that kinks occur in nutation if and only if = s.

(a) Using the notation and initial conditions of the example in Section 8.7.6, prove that kinks occur in nutation if and only if ∆Ω = ±Ωs. (A kink is where the plot of θ(t) vs. Ф(t) has a discontinuity in its slope.)
(b) Prove that these kinks are in fact cusps. (A cusp is a kink where the plot reverses direction in the Ф-θ plane.)