#undulation

There are many different types of stages upon which your butt can be handed to you, such as the Great Wall's stairs, a moving raft, and a sloped roof. You'd better make use of the new Dodge button if you don't want this to happen.

Snakes use at least five unique modes of terrestrial locomotion. The kind of locomotion a snake uses in any particular instance depends on several factors such as the kind of surface it is crawling on and its speed. In fact, an individual snake can use most or all of the five modes, and can even use two modes in different parts of the body. Below are descriptions of the various modes of snake locomotion and a brief bibliography.

But first, the locomotor mode of most limbless lizards is Simple Undulation. Simple undulation is characterized by waves of lateral bending being propagated along the body from head to tail. The bends push laterally against surface objects, but do not deform locally around them, and usually slip out of contact quickly; in this way, simple undulation differs from the more complex Lateral Undulation of snakes (see below). Most elongate and limbless lizards use simple undulation when crawling on the surface of the ground; however, a few species use the more complex mode of lateral undulation that snakes use.

Lateral Undulation is the common serpentine locomotion of snakes. In lateral undulation, as in simple undulation, waves of lateral bending are propagated along the body from head to tail. But lateral undulation is unique in that whenever a bend contacts a surface object, such as a rock or stick, it exerts force against it and deforms locally around it. Whenever a snake pushes against multiple objects simultaneously, the lateral force vectors cancel each other, leaving a resultant vector that propels the snake forward; postural adjustment around each object gives the snake even finer control over the direction of force exertion. Force exertion against each object is inversely proportional to the number of objects being pushed against simultaneously by the snake, but total force is roughly constant for a given speed and substrate. In lateral undulation, the large dorsal muscles are activated sequentially along the body. The muscles are active unilaterally in each bend, from the convex part of a bend forward to the straight or concave part of the bend. As the snake progresses, each point along its body follows along the path established by the head and neck, like the cars of a train following the engine as it moves along the track (although the propulsive mechanism is very different); thus, sliding friction is a critical component of lateral undulation. The local adjustment of curvature around each point of contact with an external object indicates a high degree of sensory-motor control, unique to snakes and a few species of limbless lizards.

Sidewinding is used by many snakes crawling on smooth or slippery surfaces, but is best known in the sidewinder rattlesnake (Crotalus cerastes) and a few desert vipers of Africa and Asia. Sidewinding is similar to lateral undulation in the pattern of bending, but differs in three critical ways: First, each point along the body is sequentially placed in static (rather than sliding) friction with the substrate. Second, segments of the body are lifted off the ground between the regions in static contact with the ground. Thus, the body sort of rolls along the ground from neck to tail, forming a characteristic track (that is proportional to body length) in sand; after being lifted off the ground and set down again a short distance away, the front part of the body begins a new track while the rear part of the body completes the old track. Third, because of the static contact and lifting of the body, the snake travels roughly diagonally relative to the tracks it forms on the ground. Muscle activity during sidewinding is similar to that in lateral undulation except that some muscles are also active bilaterally in the regions of trunk lifting.

Concertina locomotion involves alternately pulling up the body into bends and then straightening out the body forward from the bends. The front part of the body then comes to rest on the surface and the back part of the body is pulled up into bends again, and so forth. The bends may push laterally against the sides of a tunnel or vertically against the ground to keep the body from slipping. Thus, static friction is critical to concertina locomotion. Concertina locomotion is used in crawling through tunnels or narrow passages and in climbing. In concertina locomotion, blocks of muscles are activated simultaneously, and unilaterally, in regions of bending and of static contact with the sides of a tunnel.

Rectilinear locomotion is movement in a straight line. It is used mainly by large snakes such as large vipers, boas, and pythons. In rectilinear locomotion, the belly scales are alternately lifted slightly from the ground and pulled forward, and then pulled downward and backward.  But because the scales "stick" against the ground, the body is actually pulled forward over them.  Once the body has moved far enough forward to stretch the scales, the cycle repeats.  This cycle occurs simultaneously at several points along the body.  Static friction is the dominant type of friction involved in rectilinear locomotion. Unlike lateral undulation and sidewinding, which involve unilateral muscle activity that alternates from one side of the body to the other, rectilinear locomotion involves bilateral activity of the muscles that connect the skin to the skeleton. One set of these muscles lifts the belly scales up and pulls them forward and another set of muscles pulls the them downward and backward. Blog owner @scoriarose's addition: Snakes have ribs with ball joints which allows them to function similar to legs, and are also relevant to this motion. For more information please see this: https://www.tumblr.com/scoriarose/756537189019648000

Slide-pushing involves vigorous undulations of the body that slide widely over the surface. Slide-pushing is used when a snake on a smooth surface is startled and tries to escape quickly, but slips over the surface. In slide-pushing, irregular bends of the body and tail press vertically on the surface at different points; although the body slips on the surface, it pushes down with enough force to move the center of mass in a quasi-regular, often step-like, pattern.  Thus the snake progresses irregularly by slipping along the ground. Sliding friction is most important in slide-pushing, although there may be occasional moments of static contact. The patterns of muscle activity during slide-pushing are unknown.

Original article written by Brad Moon, 2001 References Below Cut

moving spots of light.

We have a chicken-and-egg situation in Fluid Mechanics. A deep question of which came first. A wavy morphology of the bottom of this very shallow stream would of course cause the surface of the water too to take on this wavy form. But, equally, it could be argued that the undulations of this flowing fluid could carve out the wavy bottom, in such an inextricably intertwined situation of cause exchanging places with consequence as to constitute a complex conceptual conundrum. A queer case of the sculptor exchanging roles with the sculpted.

Be that as it may, there is no dubitation regarding the elegance and beauty of this wavy water surface, it as perfect and pulchritudinous as a mathematical function translated into geometry.

Two other salient points  may be added to the above observation. Note the extraordinary surface detail of that wavy surface. Far from being smooth it is jam-packed with details, ridged and ribbed with complex longitudinal contours.

Furthermore, while that waveform is laminar, without breakage, it  was on occasion observed to break into spontaneous turbulence as seen in one of the photos, a turbulence that just as abruptly disappeared restoring the hitherto unbroken surface, as the photo after the turbulent foam photo shows. The turbulence may be interpreted  as a particular example of Le Chatelier’s Principle, namely that the system will react in a manner as to oppose a change, in this case the fast flow. It can also be interpreted as a type of inertia, that is a resistance to being put into motion.

The undulations gain their maximum magnitude just before the stream debouches out into the surf.