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.
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