Limbless undulatory propulsion on land
Original Entry by Michelle Borkin, AP225 Fall 2009
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008.
undulatory locomotion, Viscoelastic
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)
The lateral undulatory motion works by propagating a wave down the creature's body. As show in Figure 1, the lateral (side-ways) forces brace the body (the motion in each lateral direction cancels itself out) against the substrate thus allowing the in-plane forces to propel it in a forward (or backward) direction. In part (a), the thickness of the black line illustrates the muscle contractions and black dots the points of inflection. This paper approximates this kind of movement on a solid substrate and takes into account frictional forces.