[I'm not placing any judgment on snakes' movement technique; I just couldn't resist the Harry Potter pun!]
Along with her obvious chihuahua roots, we suspect Lorna has some terrier in her, due to her dogged (heh) attempts to catch small animals, including (to my mother-in-law's horror) snakes!
During a walk this past week, I saw her lunge forward and I instinctively yanked back on the leash to see this fellow slithering away. I was hypnotized by the rhythmic motion, and was immediately curious how it worked.
Searching a bit online, I found a paper called
The mechanics of slithering locomotion, which seemed like exactly what I wanted to know. The idea the paper puts forward is that the friction between the snake and the ground is different depending on which way it slides: There's less grip along the length of the snake than across it. You can see the difference in the pattern of scales:
 |
| Figure 1 from the paper |
The paper goes into a lot of detail about making the snakes move at different angles and, of course drugging them for pictures, but I was curious if I could make a simple model based solely on the idea of direction-dependent friction.
Suppose the snake moves forward at a constant velocity, while moving sinusoidally in the transverse direction. We can write this as a parametric equation:
where
v_x is the forward velocity, and
A and
ω are the amplitude and frequency of the side-to-side motion. Differentiating twice will give us the acceleration needed to maintain this motion. Of course, since the
x-velocity is constant, the acceleration is zero, so turning to
y,
That's in terms of the direction lateral to the snake's overall motion, but that's not what we're interested in. We want the acceleration in terms of the snake's body direction. The direction of the snake can be written as
We can plug in the derivative, normalize the vector, then use the equations
to get the components of acceleration parallel and normal to the snake. That gets a bit messy though, so I'll skip to the nifty animation:
As you can see, the forces perpendicular to the body (red) are much larger than the ones parallel (blue), requiring more friction as the paper found.
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