title: Optimizing snake locomotion on an inclined plane.
abstract: 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.
authors.affiliation: Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA and School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
authors.forename: Xiaolin
authors.initials: X
authors.lastname: Wang
authors.affiliation: Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA and Department of Mathematics and Statistics, University of Toledo, Toledo, Ohio 43606, USA.
authors.forename: Matthew T
authors.initials: MT
authors.lastname: Osborne
authors.affiliation: Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA.
authors.forename: Silas
authors.initials: S
authors.lastname: Alben
mesh_terms: D000818:Animals; D049628:Body Size / Q000502:physiology*; D003198:Computer Simulation; D017276:Friction; D005684:Gait / Q000502:physiology*; D008124:Locomotion / Q000502:physiology*; D008954:Models, Biological; D012911:Snakes / Q000502:physiology*