Marion, Problem 2-42

A solid cube of uniform density and sides of b is in equilibrium on top of a sphere of radius R. Under what conditions is the equilibrium stable or not stable?

Manipulate[
Plot[(1/2)((1+(1/α))Cos[θ]+ θ Sin[θ]),{θ,-(π/3),(π/3)},
PlotRange->{{-(π/3),(π/3)},{0,3}},
Ticks->{Range[-(π/3),(π/3),(π/12)],Range[0,3,1]},
Frame->True,
FrameLabel->{"θ","(U/mgD)"},
GridLines->{Range[-(π/3),(π/3),(π/12)],Range[0,3,1]},
PlotStyle->Thick
],
{{α,3,"(D/b)"},0.2,8,0.1, Appearance->"Labeled"}
]