Body-attitude coordination in arbitrary dimension

Abstract

We consider a system of self-propelled agents interacting through body attitude coordination in arbitrary dimension n ≥ 3. We derive the formal kinetic and hydrodynamic limits for this model. Previous literature was restricted to dimension n = 3 only and relied on parametrizations of the rotation group that are only valid in dimension 3. To extend the result to arbitrary dimensions n ≥ 3, we develop a different strategy based on Lie group representations and the Weyl integration formula. These results open the way to the study of the resulting hydrodynamic model (the "Self-Organized Hydrodynamics for Body orientation (SOHB)") in arbitrary dimensions