  In autonomous differential equations where a single first integral is
present, periodic orbits are well-known to belong to one-parameter families,
parameterized by the first integral's values. This paper shows that this
characteristic extends to a broader class of conservative hybrid dynamical
systems (cHDSs). We define recurrent cHDSs to study periodic orbits,
introducing the concept of a hybrid first integral to characterize conservation
in these systems. Additionally, our work presents a methodology that utilizes
numerical continuation methods to generate these periodic orbits, building upon
the concept of normal periodic orbits. We specifically compare state-based and
time-based implementations of an cHDS as an important application detail in
generating periodic orbits. Furthermore, we showcase the continuation process
using exemplary conservative mechanical systems with impulsive dynamics.
