N-Body Choreographies
The choreographies shown in the animations are all found by minimizing the action on a space of finite Fourier series, subject to the symmetry constraints in each case. The inter-particle force is Newtonian: it varies as the inverse square of the distance (like gravity). More details are given in the paper (see below for link).
Local Resources
- Animations illustrating the paper below (thanks to Dan Gries)
- Download paper by Montaldi and Steckles from CUP (open access)
- The maple worksheet (Maple 13) used for the calculations for the animation and the figures in the paper (best to right-click and download).
Other resources
- Richard Montgomery's scholarpedia article (2010)
- Java applet by Charlie McDowell, showing a number of choreographies, all found numerically by Carles Simó
- Many 3-body choreographies, by Richard Montgomery
- Davide Ferrario's 3-D choreographies (movies)
- Gregory Minton's design-your-own-choreography webpage, with many crown-sourced examples
home page
18 April, 2013