Hello there!

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:

http://nbviewer.jupyter.org/github/Obijuan/My-Ipython-notebooks/blob/master/serpenoid-curve/Serpenoid-Curve-es.ipynb

(I will probably make a document with all the documentation I´ve used as soon as I can…)

Thanks!