The stability boundary for AB integration in polar form is λT = Me jψ where M = |λT| and ψ = Arg(λT) are both functions of the angle θ as shown in Figure 8.23 for AB-2 integration. a.       Show that...

The stability boundary for AB integration in polar form is λT = Me^jψ
where M = |λT| and ψ = Arg(λT) are both functions of the angle θ as shown in Figure 8.23 for AB-2 integration.

a.       Show that M = (2 − 2 cos θ)^1/2
and ψ = tan⁻¹
(sin θ/(cos θ − 1)) for AB-1 integration.

b.      Derive Equations 8.156 and 8.158.

c.       Find M and ψ for AB-3 and AB-4 integration.