2013/02/18 by Gregory LeClaire Wagner, Gregory L. Wagner, Eric Lauga · 1 citation
Engineering · Physics and Astronomy · #Acoustics #Anatomy #Artificial intelligence #Biology #Computer science #Control theory (sociology) #Crawling #Degree (music) #Fishery #Mechanics #Micro and Nano Robotics #Modular Robots and Swarm Intelligence #Physics #Robotic Locomotion and Control #Scallop #physics.bio-ph
paper · pdf · doi:10.1016/j.jtbi.2013.01.021
published as Journal of Theoretical Biology, Volume 324, 7 May 2013, pp. 42-51
openalex publication_date 2013/02/18 · arxiv created 2013/03/11 · arxiv updated 2013/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Fluid-based locomotion at low Reynolds number is subject to the constraints of the scallop theorem, which dictate that body kinematics identical under a time-reversal symmetry (in particular, those with a single degree of freedom) cannot display locomotion on average. The implications of the theorem naturally compel one to ask whether similar symmetry constraints exist for locomotion in different environments. In this work we consider locomotion along a surface where forces are described by isotropic Coulomb friction. To address whether motions with a single degree of freedom can lead to transport, we analyze a model system consisting of two bodies whose separation distance undergoes periodic time variations. The behavior of the two-body system is entirely determined by the kinematic specification of their separation, the friction forces, and the mass of each body. We show that the constraints of the scallop theorem can be escaped in frictional media if two asymmetry conditions are met at the same time: the frictional forces of each body against the surface must be distinct and the time-variation of the body-body separation must vary asymmetrically in time (so quick-slow or slow-quick in the extension-contraction phases). Our results are demonstrated numerically and interpreted using asymptotic expansions.