  We show that a two-dimensional system of flocking microswimmers interacting
hydrodynamically can be expressed using a Hamiltonian formalism. The
Hamiltonian depends strictly on the angles between the particles and their
swimming orientation, thereby restricting their available phase-space.
Simulations of co-oriented microswimmers evolve into "escalators" - sharp lines
at a particular tilt along which particles circulate. The conservation of the
Hamiltonian and its symmetry germinate the self-assembly of the observed
steady-state arrangements as confirmed by stability analysis.
