  The Kepler Mission has detected dozens of compact planetary systems with more
than four transiting planets. This sample provides a collection of close-packed
planetary systems with relatively little spread in the inclination angles of
the inferred orbits. A large fraction of the observational sample contains
limited multiplicity, begging the question whether there is a true diversity of
multi transiting systems, or if some systems merely possess high mutual
inclinations, allowing them to appear as single-transiting systems in a
transit-based survey. This paper begins an exploration of the effectiveness of
dynamical mechanisms in exciting orbital inclination within exoplanetary
systems of this class. For these tightly packed systems, we determine that the
orbital inclination angles are not spread out appreciably through
self-excitation. In contrast, the two Kepler multi-planet systems with
additional non-transiting planets are susceptible to oscillations of their
inclination angles, which means their currently observed configurations could
be due to planet-planet interactions alone. We also provide constraints and
predictions for the expected transit duration variations (TDVs) for each
planet. In these multi-planet compact Kepler systems, oscillations of their
inclination angles are remarkably hard to excite; as a result, they tend to
remain continually mutually transiting (CMT-stable). We study this issue
further by augmenting the planet masses and determining the enhancement factor
required for oscillations to move the systems out of transit. The oscillations
of inclination found here inform the recently suggested dichotomy in the sample
of solar systems observed by Kepler.
