Hoping to answer some questions, here you can find the mathematical equations describing the serpentinoid movement:
The studies by Hirose were the first ones on modelling the snake movement:
Hirose, Satoshi. Biologically Inspired Robots (Snake-like Locomotor and Manipulator.: Oxford Science Press, 1993.
You can also check this derived paper:
Simulation Study of Snake-like Robot’s Serpentine Locomotion Based on Recurdyn
; by Wang Nan, Pang Bo and Zhou Sha-Shahttp://maxwellsci.com/print/rjaset/v7-37-41.pdf)
And this documentation in Spanish by Juan González:
(I will probably make a document with all the documentation I´ve used as soon as I can…)