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5. Variations of figure-eight planar three-body motion

If we slightly vary velocities of the bodies in the initial collinear configuration from the values that provide the periodic figure-8 orbit described in the previous sections, the motion becomes irregular, though its general character persists, and the motion continues indefinitely without collisions. Now the bodies do not follow one another along exactly the same figure-8 trajectory. Each body traces a slightly different figure-8 orbit in each new cycle.

The 2nd example of this section shows a similar irregular figure-8 motion (with zero value of the angular momentum) generated by a somewhat greater variation of the initial velocities. If this variation exceeds some critical value, deviations from the figure-8 trajectories gradually increase until two bodies collide, and eventually all the bodies collide at the centre of mass of the system.

The 3rd example shows the motion in which the figure-8 trajectories of the bodies vary considerably from cycle to cycle. However, this seemingly random motion continues indefinitely and is nearly periodic: after several cycles the trajectory repeats itself almost exactly. Such a variety of the figure-8 motion is generated by initial velocities considerably different from those that produce the periodic figure-8 motion.

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Collection of remarkable three-body motions 5 of 7