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We report an experimental approach to excite, stabilize, and continuously track Bloch sphere orbits of dipolar-coupled nuclear spins in a solid. We demonstrate these results on a model system of hyperpolarized 13C nuclear spins in diamond. Without quantum control, inter-spin coupling leads to rapid spin decay in T2*=1.5ms. We elucidate a method to preserve trajectories for over T2'>27s at excursion solid angles up to 16 degrees, even in the presence of strong inter-spin coupling. This exploits a novel spin driving strategy that thermalizes the spins to a long-lived dipolar many-body state, while driving them in highly stable orbits. We show that motion of the spins can be quasi-continuously tracked for over 35s in three dimensions on the Bloch sphere. In this time the spins complete >68,000 closed precession orbits, demonstrating high stability and robustness against error. We experimentally probe the transient approach to such rigid motion, and thereby show the ability to engineer highly stable "designer" spin trajectories. Our results suggest new ways to stabilize and interrogate strongly-coupled quantum systems through periodic driving and portend powerful applications of rigid spin orbits in quantum sensing., Comment: 19 pages, 16 figures. SI: 4 pages, 7 figures. 1 anc movie file (also available on Youtube)