  Mobile users such as airplanes or ships will constitute an important segment
of the future satellite communications market. Operators are now able to
leverage digital payloads that allow flexible resource allocation policies that
are robust against dynamic user bases. One of the key problems is managing the
frequency spectrum efficiently, which has not been sufficiently explored for
mobile users.
  To address this gap, we propose a dynamic frequency management algorithm
based on linear programming that assigns resources in scenarios with both fixed
and mobile users by combining long-term planning with real-time operation. We
propose different strategies divided into proactive strategies, which stem from
robust optimization practices, and reactive strategies, which exploit a high
degree of real-time control. This represents a tradeoff between how
conservative long-time planning should be and how much real-time
reconfiguration is needed.
  To assess the performance of our method and to determine which proactive and
reactive strategies work better under which context, we simulate operational
use cases of non-geostationary constellations with different levels of
dimensionality and uncertainty, showing that our method is able to serve over
99.97\% of the fixed and mobile users in scenarios with more than 900 beams.
Finally, we discuss the trade-offs between the studied strategies in terms of
the number of served users, power consumption, and number of changes that need
to happen during operations.
