A numerical investigation of the one-dimensional newtonian three-body problem |
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Authors: | Seppo Mikkola Jarmo Hietarinta |
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Institution: | (1) Turku University Observatory and Department of Physical Sciences, University of Turku, 20500 Turku, Finland |
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Abstract: | Numerical orbit integrations have been conducted to characterize the types of trajectories in the one-dimensional Newtonian
three-body problem with equal masses and negative energy. Essentially three different types of motions were found to exist.
They may be classified according to the duration of the bound three-body state. There are zero-lifetime predictable trajectories,
finite lifetime apparently chaotic orbits, and infinite lifetime quasi-periodic motions. The quasi-periodic orbits are confined
to the neighbourhood of Schubart's stable periodic orbit. For all other trajectories the final state is of the type binary
+ single particle in both directions of time. The boundaries of the different orbit-type regions seem to be sharp. We present
statistical results for the binding energies and for the duration of the bound three-body state. Properties of individual
orbits are also summarized in the form of various graphical maps in a two-dimensional grid of parameters defining the orbit.
Supported by the Academy of Finland. |
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