  Aggregation of particles whose interaction potential depends on their mutual
orientation is considered. The aggregation dynamics is derived using a version
of Darcy's law and a variational principle depending on the geometric nature of
the physical quantities. The evolution equations that result separate into two
classes: either characteristic equations, or gradient flow equations. We derive
analytical solutions of both types of equations which are collapsed (clumped)
states and show their dynamical emergence from smooth initial conditions in
numerical simuations.
