Figure 9.

Class 2(b) example. (a) Trajectory of the gyropendulum with smooth loops passing through the origin and (b) the function $H(\tilde{t})$ with $\mathrm{\Gamma }=-1.077$ and initial conditions ${\tilde{U}}_0=2$, ${\tilde{V}}_0=3$, ${\dot{\tilde{U}}}_0=1$, ${\dot{\tilde{V}}}_0=-2$. The condition for Class 2(b) is satisfied with $H(0)=\mathrm{\Gamma }|\tilde{\mathbf{Q}}{(0)|}^2/2=-7$. In addition $H(\tilde{t})\le 0$.