Geometric mechanics and locomotion in dissipative environments

Sustained movement through complex terrain arises from the coupling of environmental interactions with cyclic self-deformation patterns generated by animals. Using both biological experiments and mathematical modeling, we explore the importance of body coordination and morphology for both limbless and limbed animals moving though a widely-encountered environment: on and within sand. Given the highly-dissipative nature of sand, we model environmental forces using granular resistive force theory (RFT) and use geometric mechanics (GM) to map local body deformations to body-frame displacements. We find that undulatory snakes and lizards swimming within sand use waveforms that produce near-maximal displacements per undulation cycle. Recently, we have found that granular RFT also applies to movement at the surface of dissipative materials, even when contact is intermittent. We apply surface granular RFT and GM to animals with cyclic ground contact patterns (e.g., legged locomotors). We find that the coordination between foot placement and spinal flexion observed in walking salamanders produces near-maximal displacements per gait cycle. These results highlight the broad applicability of these tools to understand coordination and self-deformation patterns in dissipative environments.