  We consider the synchronization of two self-excited double pendula. We show
that such pendula hanging on the same beam can have four different synchronous
configurations. Our approximate analytical analysis allows us to derive the
synchronization conditions and explain the observed types of synchronization.
We consider an energy balance in the system and describe how the energy is
transferred between the pendula via the oscillating beam, allowing thus the
pendula synchronization. Changes and stability ranges of the obtained solutions
with increasing and decreasing masses of the pendula are shown using
path-following.
