Next-generation satellite systems require more flexibility in resource management such that available radio resources can be dynamically allocated to meet time-varying and non-uniform 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 power-domain 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 terminal-timeslot 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.