Hmm, unless I'm going crazy here, we get the differential equation x'' = -(x^-2)...

		jibiki on April 21, 2009 \| parent \| context \| favorite \| on: To Everywhere in 42 Minutes Hmm, unless I'm going crazy here, we get the differential equation `x'' = -(x^-2)` x = (kt)^(2/3)(with k = (2/9)^(-3/2), not that it matters) seems to be a solution? I guess that doesn't help with the singularity, but neither does looking at energy (since you have infinite kinetic energy at the center and infinite potential energy everywhere else.)

That differential equation only holds for positive x. Try something like the following:

  x'' =  - signum(x) * (x^-2)