The equations of motion of a charged particle in the field of Yang's $\mathrm{ SU}(2)$ monopole in 5-dimensional Euclidean space are derived by applying the Kaluza-Klein formalism to the principal bundle $\mathbb{ R}^8\setminus\{ 0\}\to\mathbb{ R}^5\setminus\{ 0\}$ obtained by radially extending the Hopf fibration $S^7\to S^4$, and solved by elementary methods. The main result is that for every particle trajectory $\mathbf{ r}:I\to\mathbb{ R}^5\setminus\{ 0\}$, there is a 4-dimensional cone with vertex at the origin on which $\mathbf{ r}$ is a geodesic. We give an explicit expression of the cone for any initial conditions.
Categories: math.DS math-ph math.MP