There are two approaches to mobile users. Either you have a beam from the satellite directly track a moving user, or you have many fixed beams from the satellite and the user has to jump from one to the next as they move.
The first method was definitely used to begin with, but it doesn't scale - the satellite only has a certain number of beams available, so past a certain number of moving users it becomes necessary to use the 2nd system, which requires a very different software setup.
Eventually a hybrid system might be used, allocating per-user beams to the highest bandwidth users at the time. Per user beams can be far narrower and therefore get better SNR and more data throughput.
