Physics – Mathematical Physics
Scientific paper
2009-06-12
2009 J. Phys. A: Math. Theor. 42 395205
Physics
Mathematical Physics
Scientific paper
10.1088/1751-8113/42/39/395205
As shown by Johannes Kepler in 1609, in the two-body problem, the shape of the orbit, a given ellipse, and a given non-vanishing constant angular momentum determines the motion of the planet completely. Even in the three-body problem, in some cases, the shape of the orbit, conservation of the centre of mass and a constant of motion (the angular momentum or the total energy) determines the motion of the three bodies. We show, by a geometrical method, that choreographic motions, in which equal mass three bodies chase each other around a same curve, will be uniquely determined for the following two cases. (i) Convex curves that have point symmetry and non-vanishing angular momentum are given. (ii) Eight-shaped curves which are similar to the curve for the figure-eight solution and the energy constant are given. The reality of the motion should be tested whether the motion satisfies an equation of motion or not. Extensions of the method for generic curves are shown. The extended methods are applicable to generic curves which does not have point symmetry. Each body may have its own curve and its own non-vanishing masses.
Fujiwara Toshiaki
Fukuda Hiroshi
Ozaki Hiroshi
No associations
LandOfFree
Three-Body Choreographies in Given Curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Three-Body Choreographies in Given Curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Three-Body Choreographies in Given Curves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-134841