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# Surfaces of separation in the Caledonian symmetrical double binary four body problem

DOI link for Surfaces of separation in the Caledonian symmetrical double binary four body problem

Surfaces of separation in the Caledonian symmetrical double binary four body problem book

# Surfaces of separation in the Caledonian symmetrical double binary four body problem

DOI link for Surfaces of separation in the Caledonian symmetrical double binary four body problem

Surfaces of separation in the Caledonian symmetrical double binary four body problem book

## ABSTRACT

The four-body Caledonian problem introduced by the authors enables considerable simplification to be made particularly in the form of the Caledonian Symmetrical Double Binary Problem (CSDBP). This chapter shows how the CSDBP model can be used to obtain surfaces of separation which enable predictions to be made of the possible paths of evolution the initial hierarchy of the four-body system can take. The CSDBP is formulated by using all possible symmetries. The main feature of the model is its use of two types of symmetry: past-future symmetry and dynamical symmetry. The CSDBP is three-dimensional and involves initially two binaries, each binary having components of unequal masses, but the same two mass values as the other binary. Additionally, the ability of the Caledonian problem to utilise a large number of initial parameters and still preserve symmetry enables a large family of such models to be studied.