  Many recent observational studies have concluded that planetary systems
commonly exist in multiple-star systems. At least ~20% of the known extrasolar
planetary systems are associated with one or more stellar companions. The
orbits of stellar binaries hosting planetary systems are typically wider than
100 AU and often highly inclined with respect to the planetary orbits. The
effect of secular perturbations from such an inclined binary orbit on a coupled
system of planets, however, is little understood theoretically. In this paper
we investigate various dynamical classes of double-planet systems in binaries
through numerical integrations and we provide an analytic framework based on
secular perturbation theories. Differential nodal precession of the planets is
the key property that separates two distinct dynamical classes of multiple
planets in binaries: (1) dynamically-rigid systems in which the orbital planes
of planets precess in concert as if they were embedded in a rigid disk, and (2)
weakly-coupled systems in which the mutual inclination angle between initially
coplanar planets grows to large values on secular timescales. In the latter
case, the quadrupole perturbation from the outer planet induces additional
Kozai cycles and causes the orbital eccentricity of the inner planet to
oscillate with large amplitudes. The cyclic angular momentum transfer from a
stellar companion propagating inward through planets can significantly alter
the orbital properties of the inner planet on shorter timescales. This
perturbation propagation mechanism may offer important constraints on the
presence of additional planets in known single-planet systems in binaries.
