N-body choreography
When two bodies orbit around each other in space, we know exactly what happens. The bodies trace out conic sections, they do so in accordance with Kepler’s laws, and that’s it, more or less.
When three or more bodies orbit around each other in space, things can be more complicated. In the general case, no explicit formula for the orbits exists, and we have to rely on numerical simulations.
Among all these possible orbits, though, there exist some which repeat after some time. These are called n-body choreographies (with n = the number of bodies), small islands of order in a large chaotic space of ways-things-can-be. This animation by Chris Moore shows just that.
This figure-8 animation can be perturbed in various ways. Nauenberg and Marchal independently found this version, which rotates around the x-axis and forms a continuous family of orbits connecting the figure-8 with the Lagrange orbit
More about Chris Moore's 3-Body & n-Body problems:
http://tuvalu.santafe.edu/~moore/gallery.html
Watch video:
Twenty one body Newtonian choreography; black
More about Nauenberg and Marchal version:
http://iopscience.iop.org/1538-3881/124/4/2332/fulltext/
More about Lagrangian point:
http://en.wikipedia.org/wiki/Lagrangian_point
Nice post :-)
ReplyDeleteDon Inbody Your namesake?? :)
ReplyDeleteIndeed, today I learned a few more things about Lagrangian points Hudson Ansley =)
ReplyDeleteAnd danke
The motion is exactly like if one were to joggle 3 balls in a perfectly stable air vortex - awesome :D
ReplyDeleteGreat post, thank you.
ReplyDeleteI do not speak English so excuse my translation: In this example, increase the average number of bodies or limiting condition for the smallest distance between two adjacent objects which may not be less than the diameter of the largest element. Thank you. Mickey
ReplyDeleteCorina Marinescu Since I can comment on this post, I'm going to take this opportunity to ask if you would be so kind as to allow me to post on your other excellent posts. I promise not to abuse the privilege :-)
ReplyDeleteOf course, you can
ReplyDelete