Geodesics from classical double copy

We extend the Kerr-Schild double copy to case of a probe particle moving in background. In particular, we solve Wong's equations for test color charge Coulomb non-Abelian potential ($\sqrt{\text{Schw}}$) and on equatorial plane generated by rotating disk known as single Kerr background ($\sqrt{\text{Kerr}}$). The orbits, corresponding geodesics gravity side, feature elliptic, circular, hyperbolic plunge behavior charged particle. then find new map between conserved charges gauge theory side which enables us fully recover geodesic Schwarzschild Kerr. Interestingly, works naturally both bound unbound orbits.