Figure 8.

Class 2(a) examples. (a) Cusp trajectory of the gyropendulum and (b) the function $H(\tilde{t})$ with $\mathrm{\Gamma }=2.8$ and initial conditions ${\tilde{U}}_0=2$, ${\tilde{V}}_0=3$, ${\dot{\tilde{U}}}_0=1$, ${\dot{\tilde{V}}}_0=-2$. The condition for cusps is satisfied with $H(0)=-\mathrm{\Gamma }|\dot{\tilde{\mathbf{Q}}}{(0)|}^2/2=-7$. Here $H(\tilde{t})\le 0.$ (c) Cusp trajectory of the gyropendulum and (d) the function $H(\tilde{t})$ with $\mathrm{\Gamma }=-0.4$ and initial conditions ${\tilde{U}}_0=2$, ${\tilde{V}}_0=3$, ${\dot{\tilde{U}}}_0=1$, ${\dot{\tilde{V}}}_0=2$. The condition for cusps is satisfied with $H(0)=-\mathrm{\Gamma }|\dot{\tilde{\mathbf{Q}}}{(0)|}^2/2=1$. Here $H(\tilde{t})\ge 0$.