Next-generation satellite systems require more flexibility in resource management such that available radio resources can be dynamically allocated to meet time-varying and nonuniform traffic demands. Considering potential benefits of beam hopping (BH) and non-orthogonal multiple access (NOMA), we exploit the time-domain flexibility in multi-beam satellite systems by optimizing BH design, and enhance the powerdomain flexibility via NOMA. In this paper, we investigate the synergy and mutual influence of beam hopping and NOMA. We jointly optimize power allocation, beam scheduling, and terminaltimeslot assignment to minimize the gap between requested traffic demand and offered capacity. In the solution development, we formally prove the NP-hardness of the optimization problem. Next, we develop a bounding scheme to tightly gauge the global optimum and propose a suboptimal algorithm to enable efficient resource assignment. Numerical results demonstrate the benefits of combining NOMA and BH, and validate the superiority of the proposed BH-NOMA schemes over benchmarks.