mathematical equations for galloping model of limbs in robots

I'm by no means an expert in biomimicry, but I think this paper form
the good folks at the Ambulatory Robotics Laboratory might shed some
light on the subject.

http://www.cim.mcgill.ca/~jasmith/docs/AMAM2003_paper.pdf

there are also quite a few links and terms in that PDF that may help
in further searches.

CG animation for cartoons goes into this area, especially where
splines based on "keys" points are mixed with splines of other gaits
such as walking, and seamlessly blended. www.softimage.com is a
leading software featuring this function. If you're referring to a
calculation that for a given speed would provide the given curve --
suddenly I wish I'd taken calculus, it sounds kind of like a homework
problem.

The easy way to do it is to use "inverse kinematics". Set up a model
of the beast in terms of masses, links, motor forces, springs and
gravity etc. and see how it reacts to tasks that you set it. Animators
use it when they want natural movement.
http://www.cs.ubc.ca/~van/cpsc533B/Vjan2003/projects/HB/Motion%20Doodles%20for%20Quadrupeds.pdf