  We introduce a simple model of self-propelled agents connected by linear
springs, with no explicit alignment rules. Below a critical noise level, the
agents self-organize into a collectively translating or rotating group. We
derive analytical stability conditions for the translating state in an elastic
sheet approximation. We propose an elasticity-based mechanism that drives
convergence to collective motion by cascading self-propulsion energy towards
lower-energy modes. Given its simplicity and ubiquity, such mechanism could
play a relevant role in various biological and robotic swarms.
