We derive and test two new symplectic integrator algorithms, suitable for studying planetary accretion in binary star systems. The algorithms incorporate the hierarchical nature of stable planetary orbits in binary star systems. In one case, planets orbit a single star, perturbed by a distant companion; in the second case, planets orbit both binary members. Each algorithm integrates close encounters between planets symplectically using a hybrid symplectic scheme.
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Chambers et al. (2002) studied this question.
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