Figure 10
From: Controlling the motion of gravitational spinners and waves in chiral waveguides
Class 3 examples. (a) Smooth trajectories of the gyropendulum not passing through the origin, and (b) the function \(H(\tilde{t})\) with parameter values \(\Gamma =1\) and initial conditions \(\tilde{U}_0 =2\), \(\tilde{V}_0 = 3\), \(\dot{\tilde{U}}_0 =-1\), \(\dot{\tilde{V}}_0 = 2\). The Class 3 conditions are satisfied with \(H(0)=7\), \(- \Gamma |\dot{\tilde{{\textbf {Q}}}}(0)|^2/2=-2.5\) and \(\Gamma |{\tilde{{\textbf {Q}}}}(0)|^2/2=6.5.\) (c) Smooth trajectories of the gyropendulum not passing through the origin, and (d) the function \(H(\tilde{t})\) with parameter values \(\Gamma =1\) and initial conditions \(\tilde{U}_0 =2\), \(\tilde{V}_0 = 3\), \(\dot{\tilde{U}}_0 =1\), \(\dot{\tilde{V}}_0 = -2\). The Class 3 conditions are satisfied with \(H(0)=-7\), \(- \Gamma |\dot{\tilde{{\textbf {Q}}}}(0)|^2/2=-2.5\) and \(\Gamma |{\tilde{{\textbf {Q}}}}(0)|^2/2=6.5.\) The solid arrows indicate the direction of spin of the gyroscopic spinner, and the hollow arrows show the orientation of motion for each respective trajectory of the gyropendulum.
