Illustrations of the New Sitnikov formation motion

for the 3-body problem

From here you can download a zipped file which must be unzipped into a folder of your choice. Then the files (courtesy to Mark Frenkel) from this folder must be loaded as scripts by the TCenter.exe program. These scripts by default are stereo presentations. To view stereo images, you need anaglyphic Red/Blue glasses. Such glasses may be ordered here: look for the Red/Blue type (not Red/Cyan).

If you have anaglyphic glasses, click  3D stereo images (to learn about the optimal viewing conditions and see a few examples of stereo images). Without the anaglyphic glasses, you may view non-planar curves also in conventional axonometry setting the checkbox Axonomet. 

Fig. 12 (in stereo)

Fig 12 (in axonometry)

Fig. 12 as a movie SitnikovFlower.mp4

Fig. 12, the beginning stage.

The n+1 body Sitnikov case

Here we consider a generalization of the original Sitnikov case for n equal masses initially in the Lagrange formation of a regular n-polygon plus the body number n+1 on the perpendicular at the center of the polygon moving only along this perpendicular. The original Sitnikov case corresponds to n=2.

A picture of the n+1 body Sitnikov case for n=5, all 6 bodies having equal masses, the script file 3DSitn5.scr.

The vertical component z of the initial velocities was set so that the impulse of the system be zero and the 5 bodies stay in a plane. As the body oscillating vertically has nonzero mass, the plane containing 5 bodies oscillates vertically too. In this case the oscillation is chaotic. Here you can see the motion of this system as a movie.