Symbol sequences and orbits of the free-fall three-body problem
Kiyotaka Tanikawa and Seppo Mikkola
自由落下三体問題の記号列と軌道
谷川清隆、セッポ ミッコラ
Publ. Astron. National astronomical Observatory of Japan Vol.67,
Issue 6, id.11510 pp. (2015)
Using the symbols and symbol sequences along the orbits introduced
in our preceding work, we numerically study the orbital structure of
the free-fall three-body problem. We confirm and re-interpret
the results obtained by us before.
We describe the overall structure of the plane.
It turns out that the structures of the initial condition plane can be
systematically obtained with symbol sequences.
Then, we obtain the structure of two interesting local regions:
the isosceles and collinear boundaries of the plane.
We present sequences of triple collision orbits and
periodic orbits on these boundaries.
We additionally argue that stable and/or unstable manifolds of
the two-body collision manifolds connect different
triple collision manifolds.
Using the symbols and symbol sequences along the orbits
introduced in our preceding work,
we numerically study the orbital structure of
the free-fall three-body problem.
We confirm and re-interpret the results obtained by us before.
We describe the overall structure of the plane.
It turns out that the structures of
the initial condition plane can be systematically obtained
with symbol sequences.
Then, we obtain the structure of two interesting local regions:
the isosceles and collinear boundaries of the plane.
We present sequences of triple collision orbits and
periodic orbits on these boundaries.
We additionally argue that stable and/or unstable manifolds of
the two-body collision manifolds connect different
triple collision manifolds.
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