Tidal locking in structured active matter on elastic surfaces

Agents in active matter are typically rigid and thus treated as point particles. However, active matter agents can also contain structure such that an individual can be compressed or stretched. In the presence of external fields, the coupling between the structured agent and its environment can deform the agent as well as affect its trajectory. Here, we use a recently developed system in which 200-gram, 10 cm diameter wheeled vehicles locomote at constant speed on a large deformable spandex membrane (diameter 2.4 m). Agents exhibit rich dynamics, including precessing orbits of a single rigid body; the dynamics can be mapped to motion in a "fiducial" curved spacetime (Li et al., PNAS, 2022). We use this system to explore properties of structured active matter in a spatially varying field by connecting two vehicles via a linear spring and study the orbital dynamics of the vehicles on the membrane. For a range of relative car speeds the entity can be captured in a tidally-locked trajectory such that the same vehicle remains closest to the central depression during a trajectory, analogous to the state where the Moon maintains the same side facing towards the Earth. We posit that the membrane and its gradient field are integral to creating the tidal-locking trajectories, as tidal-locking is not observed without the membrane. Further, we observe that the capture and attraction to the tidally-locked state is modulated by the spring's restoring force, and the rate of capture depends on the spring constant and relative car speeds.