This paper extends recent work in demonstrating magnetic manipulation of conductive, nonmagnetic objects using rotating magnetic dipole fields. The current state of the art demonstrates dexterous manipulation of solid copper spheres with all object parameters known a priori. Our approach expands the previous model that contained three discrete modes to a single, continuous model that covers all possible relative positions of the manipulated object relative to the magnetic field source. We further leverage this new model to examine manipulation of spherical objects with unknown physical parameters, by applying techniques from the online-optimization and adaptive-control literature. Our experimental results validate our new dynamics model, showing that we get comparable or improved performance to the previously proposed model, while solving a simpler optimization problem for control. We further demonstrate the first physical magnetic control of aluminum spheres, as previous controllers were only physically validated on copper spheres. We show that our adaptive control framework can quickly acquire accurate estimates of the true spherical radius when weakly initialized, enabling control of spheres with unknown physical properties. Finally, we demonstrate that the sphericalobject model can be used as an approximate model for adaptive control of nonspherical objects by performing the first magnetic manipulation of nonspherical, nonmagnetic objects.