The following movies are periodic solutions bifurcated from the figure-eight choreographic solutions to the equation of motion
d2qi/dt2 = -∂U/∂qi, U=Σi>ju(qi-qj), i = 0,1,2
See preprint on initial conditions.
Homogeneous potential
Homogeneous potential
u(r)=-1/ra
Dxy bifurcated from a=0.9966
Dxy bifurcated from a=0.9966
(Simó's H)
Bifurcation from a=1.3424
Bifurcation from a=1.3424
The Lennard-Jones-type potential
The Lennard-Jones-type potential
u(r)=-1/r6+1/r12
Dxy from α+ at T=16.878
Dxy from α+ at T=16.878
Dxy from α- at T=14.836
Dxy from α- at T=14.836
Bifurcation from α+ at T=16.111
Bifurcation from α+ at T=16.111
Bifurcation from α- at T=14.861
Bifurcation from α- at T=14.861
Cx bifurcated from α- at T=14.595
Cx bifurcated from α- at T=14.595
C2 bifurcated from α+ at T=18.615
C2 bifurcated from α+ at T=18.615
Cy bifurcated from α+ at T=17.132
Cy bifurcated from α+ at T=17.132