Tidal effects on active matter induced by elastic membrane

In active matter systems, agents can interact not only via contact, but also via fields (like in movement on water or elastic surfaces). To explore active matter dynamics in the presence of time varying fields, we previously studied a 200-gram wheeled vehicle driving on a deformable spandex membrane (d=2.4m) with a static central depression (Li et al., 2019). Our system exhibits rich dynamics, including precessing orbits of a single rigid body. Motivated by internal planetary tidal disruption due to a strong gravitational force, here we develop a mechanism to connect two vehicles via a spring to emulate tidal forces on a nonrigid body. Experiments and simulations reveal three types of trajectories as we vary relative car speeds. One is a tidally locked trajectory where the same vehicle remains closest to the central depression and occurs when the outer car is slightly faster than the inner. The other two types are self-rotations where the vehicles rotate around one another while both revolve around the center, one with retrograde and one with prograde spin. In the tidally locked regime, oscillating the central depression vertically at a frequency comparable to the orbital period produces resonant pumping such that the coupled vehicles increase relative displacement over time.