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4. Figure-eight three-body motion in two frames of reference
The simulation below shows the figure-8 planar periodic three-body motion (described in the previous section) simultaneously in two frames of reference: the inertial centre-of-mass frame (upper) and the frame associated with one of the bodies (lower).
After T/3 time interval (one-third of the total period T), the bodies again occur on the same straight line as in the initial configuration, but in a different order. There is one more (symmetric) straight line on which the bodies simultaneously occur in T/6 time interval after the first collinear configuration. In the meantime (after T/12) the bodies form an isosceles triangular configuration.
If we change slightly the initial conditions (preserving the zero value of the angular momentum), the motion becomes irregular, though its general figure-8 character persists, and the motion continues indefinitely without collisions. That is, the figure-8 motion is stable with respect to small perturbations of the velocities and positions.
Next section shows several variations of the figure-8 motion theme.
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Collection of remarkable three-body motions – 4 of 7