Guo Z V, Mahadevan L
School of Engineering and Applied Sciences and Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA.
Proc Natl Acad Sci U S A. 2008 Mar 4;105(9):3179-84. doi: 10.1073/pnas.0705442105. Epub 2008 Feb 28.
We analyze the lateral undulatory motion of a natural or artificial snake or other slender organism that "swims" on land by propagating retrograde flexural waves. The governing equations for the planar lateral undulation of a thin filament that interacts frictionally with its environment lead to an incomplete system. Closures accounting for the forces generated by the internal muscles and the interaction of the filament with its environment lead to a nonlinear boundary value problem, which we solve using a combination of analytical and numerical methods. We find that the primary determinant of the shape of the organism is its interaction with the external environment, whereas the speed of the organism is determined primarily by the internal muscular forces, consistent with prior qualitative observations. Our model also allows us to pose and solve a variety of optimization problems such as those associated with maximum speed and mechanical efficiency, thus defining the performance envelope of this mode of locomotion.
我们分析了天然或人造蛇类或其他细长生物体在陆地上通过传播逆行弯曲波进行“游动”时的侧向波动运动。与周围环境存在摩擦相互作用的细丝平面侧向波动的控制方程导致了一个不完整的系统。考虑到内部肌肉产生的力以及细丝与周围环境的相互作用的封闭条件导致了一个非线性边值问题，我们使用解析方法和数值方法相结合来求解该问题。我们发现，生物体形状的主要决定因素是其与外部环境的相互作用，而生物体的速度主要由内部肌肉力量决定，这与先前的定性观察结果一致。我们的模型还使我们能够提出并解决各种优化问题，例如与最大速度和机械效率相关的问题，从而定义这种运动模式的性能范围。
