Introduction to Classical Mechanics · Problem 9.25

Angular momentum, Part II (General L) — Morin

Physics — Mechanics · nutation-cusps

Problem

((a)) Using the notation and initial conditions in the example in Section 9.7.7, prove that kinks occur in nutation if and only if

\Delta\Omega = \pm\Omega_s

. A kink is where the plot of

\theta(t)

vs.\

\phi(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

\phi

\theta

plane.