  Inspired by the experimental results of Cuevas et al. (Physical Review
Letters 102, 224101 (2009)), we consider theoretically the behavior of a chain
of planar rigid pendulums suspended in a uniform gravitational field and
subjected to a horizontal periodic driving force applied to the pendulum
pivots. We characterize the motion of a single pendulum, finding bistability
near the fundamental resonance, and near the period-3 subharmonic resonance. We
examine the development of modulational instability in a driven pendulum chain
and find both a critical chain length and critical frequency for the appearance
of the instability. We study the breather solutions and show their connection
to the single pendulum dynamics, and extend our analysis to consider
multi-frequency breathers connected to the period-3 periodic solution, showing
also the possibility of stability in these breather states. Finally we examine
the problem of breather generation and demonstrate a robust scheme for
generation of on-site and off-site breathers.
