Figure 5.

(a) A gyropendulum includes a gyroscopic spinner connected to the tip of a rod. The rod is hinged at its base which is located at the origin of the fixed coordinate system Oxyz. The gyroscopic spinner is shown in the local coordinate system $O^{\prime }{x}^{\prime }{y}^{\prime }{z}^{\prime }$, which moves with the spinner as it nutates through an angle $\theta$, precesses through an angle $\varphi$ and spins through an angle $\psi$. The axes of the rod and the spinner are assumed to be aligned at any instant of time. (b) Experimental observation and analytical prediction for cusp-shaped trajectories; the video of the motion is provided in the electronic supplementary material.