On the left, the stability region of the angular velocity |$\theta _d^*(E_s)$| with |$\alpha =\pi /9$| for varying energy |$E_s$| from |$1.45$| to |$3$|⁠. The horizontal line shows the case of |$\theta _d^*=\sqrt{\cos \alpha }=0.9694$|⁠. On the right, the stability region of the angular velocity |$\theta _d^*(\alpha )$| with |$E_s=1.8$| for varying angles of attack |$\alpha $| from |$10^{\circ }(=\pi /18)$| to |$30^{\circ }(=\pi /6)$|⁠. The upper and lower limits are |$\left (\theta _d^*\right )^+$| and |$\left (\theta _d^*\right )^-$|⁠, respectively. The region of stable fixed points, with eigenvalues |$-1<f^{\prime}(Y^*) < 1$|⁠, is marked in grey. The region of unstable fixed points with eigenvalues |$f ^{\prime}(Y^*)>1$| is marked in blue. |$f^{\prime}$| is the eigenvalue notation used in the legend.