Point vortices on a cylinder (periodic strip) are studied geometrically. The Hamiltonian formalism is developed, a nonexistence theorem for relative equilibria is proved, equilibria are classified when all vorticities have the same sign, and several results on relative periodic orbits are established, including as corollaries classical results on vortex streets and leapfrogging.
- Conservation laws
- Geometric mechanics
- Hamiltonian systems with symmetry
- Point vortices