Hiroshi FUKUDA

(2019.01.09)

Preprint arXiv:1901.00115

The following movies are periodic solutions bifurcated from the figure-eight choreographic solutions to the equation of motion

See arXiv:1901.00115 on initial conditions.d^{2}/^{}q_{i}dt^{2}= -∂U/∂q,_{i}U=Σ_{i>j}u(q-_{i}q),_{j}i= 0,1,2

u(r)=-1/r^{a}

Dbifurcated from_{xy}a=0.9966

a=0.9766, Δt=T/12/,T=1

a=1.0166, Δt=T/12/,T=1

a=1.0000 (Simó's H), Δt=T/12/,T=1## Bifurcation from

a=1.3424

Dat_{x}a=1.3425, Δt=T/12/,T=1

Dat_{2}a=1.3425, Δt=T/12/,T=1

u(r)=-1/r+1/^{6}r^{12}

Dfrom α_{xy}_{+}atT=16.878

## From the left side

, Δt=T/12/,T=20## From the right side

, Δt=T/12/,T=20

Dfrom α_{xy}_{-}atT=14.836

## From the left side

, Δt=T/12/,T=20## From the right side

, Δt=T/12/,T=20## Bifurcation from α

_{+}atT=16.111

D_{x}, Δt=T/12/,T=20

D_{2}, Δt=T/12/,T=20## Bifurcation from α

_{-}atT=14.861

D_{x}, Δt=T/12/,T=20

D_{2}, Δt=T/12/,T=20

Cbifurcated from α_{x}_{-}atT=14.595, Δt=T/12/,T=20

Cbifurcated from α_{2}_{+}atT=18.615, Δt=T/12/,T=20

Cbifurcated from α_{y}_{+}atT=17.132, Δt=T/12/,T=20