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We extend the formalism of a previous paper to include the effects of flybysand instantaneous perturbations such as supernovae on the long-term secularevolution of hierarchical multiple systems with an arbitrary number of bodiesand hierarchy, provided that the system is composed of nested binary orbits. Tomodel secular encounters, we expand the Hamiltonian in terms of the ratio ofthe separation of the perturber with respect to the barycentre of the multiplesystem, to the separation of the widest orbit. Subsequently, we integrate overthe perturber orbit numerically or analytically. We verify our method forsecular encounters, and illustrate it with an example. Furthermore, we describea method to compute instantaneous orbital changes to multiple systems, such asasymmetric supernovae and impulsive encounters. The secular code, withimplementation of the extensions described in this paper, is publicly availablewithin AMUSE, and we provide a number of simple example scripts to illustrateits usage for secular and impulsive encounters, and asymmetric supernovae. Theextensions presented in this paper are a next step toward efficiently modelingthe evolution of complex multiple systems embedded in star clusters.

monthly notices of the royal astronomical society

Secular dynamics of hierarchical multiple systems composed of nested  binaries, with an arbitrary number of bodies and arbitrary hierarchical  structure. II. External perturbations: flybys and supernovae