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This article extends recent work in magnetic manipulation of conductive, nonmagnetic objects using rotating magnetic dipole fields. Eddy-current-based manipulation provides a contact-free way to manipulate metallic objects. We are particularly motivated by the large amount of aluminum in space debris. We previously demonstrated dexterous manipulation of solid spheres with all object parameters known a priori. This work expands the previous model, which contained three discrete modes, to a continuous model that covers all possible relative positions of the manipulated spherical object with respect 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 improved performance compared to the previously proposed model, while also solving a simpler optimization problem for control. We further demonstrate the first physical magnetic manipulation of aluminum spheres, as previous controllers were only physically validated on copper spheres. We show that our adaptive control framework can quickly acquire useful object parameters when weakly initialized. Finally, we demonstrate that the spherical-object model can be used as an approximate model for adaptive control of nonspherical objects by performing magnetic manipulation of a variety of objects for which a spherical model is not an obvious approximation.