An intrinsic aggregation model on the special orthogonal group $\mathrm{SO}(3)$: well-posedness and collective behaviours

Abstract

We investigate an aggregation model with intrinsic interactions on the special orthogonal group $SO(3)$. We consider a smooth interaction potential that depends on the squared intrinsic distance, and establish local and global existence of measure-valued solutions to the model via optimal mass transport techniques. We also study the long-time behaviours of such solutions, where we present sufficient conditions for the formation of asymptotic consensus. The analytical results are illustrated with numerical experiments that exhibit various asymptotic patterns.

47 pages, 2 figures

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Cited by in corpus (1)

• Equilibria and energy minimizers for an interaction model on the hyperbolic space