Wang Xiaolin, Osborne Matthew T, Alben Silas
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA and School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA and Department of Mathematics and Statistics, University of Toledo, Toledo, Ohio 43606, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012717. doi: 10.1103/PhysRevE.89.012717. Epub 2014 Jan 23.
We develop a model to study the locomotion of snakes on inclined planes. We determine numerically which snake motions are optimal for two retrograde traveling-wave body shapes, triangular and sinusoidal waves, across a wide range of frictional parameters and incline angles. In the regime of large transverse friction coefficients, we find power-law scalings for the optimal wave amplitudes and corresponding costs of locomotion. We give an asymptotic analysis to show that the optimal snake motions are traveling waves with amplitudes given by the same scaling laws found in the numerics.
我们开发了一个模型来研究蛇在斜面上的运动。我们通过数值计算确定了对于两种逆行行波身体形状（三角波和正弦波），在广泛的摩擦参数和倾斜角度范围内，哪种蛇的运动是最优的。在大横向摩擦系数的情况下，我们发现了最优波幅的幂律标度以及相应的运动成本。我们进行了渐近分析，以表明最优的蛇形运动是行波，其振幅由数值计算中发现的相同标度律给出。
