  Motivated by the large number of extrasolar planetary systems that are near
mean motion resonances, this paper explores a related type of dynamical
behavior known as "nodding". Here, the resonance angle of a planetary system
executes libration (oscillatory motion) for several cycles, circulates for one
or more cycles, and then enters once again into libration. This type of
complicated dynamics can affect our interpretation of observed planetary
systems that are in or near mean motion resonance. This work shows that
planetary systems in (near) mean motion resonance can exhibit nodding behavior,
and outlines the portion of parameter space where it occurs. This problem is
addressed using both full numerical integrations of the planetary systems and
via model equations obtained through expansions of the disturbing function. In
the latter approach, we identify the relevant terms that allow for nodding. The
two approaches are in agreement, and show that nodding often occurs when a
small body is in an external mean motion resonance with a larger planet. As a
result, the nodding phenomenon can be important for interpreting observations
of transit timing variations, where the existence of smaller bodies is inferred
through their effects on larger, observed transiting planets. For example, in
actively nodding planetary systems, both the amplitude and frequency of the
transit timing variations depend on the observational time window.
