Choreographic Three Bodies on the Lemniscate

Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki

We show that choreographic three bodies {x(t), x(t+T/3), x(t-T/3)} of period T on the lemniscate, x(t) = (x-hat+y-hat cn(t))sn(t)/(1+cn^2(t)) parameterized by the Jacobi's elliptic…