Relevant Science: Symplectic Integrator and the Jacobi-Gómez Morin Problem

Tuesday, February 03, 2009

$c_1 = c_4 = \frac{1}{2(2-2^{1/3})},\ \ c_2=c_3=\frac{1-2^{1/3}}{2(2-2^{1/3})},$

$d_1 = d_3 = \frac{1}{2-2^{1/3}},\ \ d_2 = -\frac{2^{1/3}}{2-2^{1/3}},\ \ d_4 = 0.$

These equations turn up in the study of the Symplectic Integrator when generalized to high orders. It is interesting that one gets cubic roots, which can be studied by Domingo Gómez Morín's methods .

Curiouser and curiouser , as Alice in Wonderland would say.