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Terrestrial experiments on active particles, such as Volvox, involvegravitational forces, torques and accompanying monopolar fluid flows. Takingthese into account, we analyse the dynamics of a pair of self-propelling,self-spinning active particles between widely separated parallel planes.Neglecting flow reflected by the planes, the dynamics of orientation andhorizontal separation is symplectic, with a Hamiltonian exactly determininglimit cycle oscillations. Near the bottom plane, gravitational torque damps andreflected flow excites this oscillator, sustaining a second limit cycle thatcan be perturbatively related to the first. Our work provides a theory fordancing Volvox and highlights the importance of monopolar flow in activematter.

Periodic Orbits of Active Particles induced by Hydrodynamic Monopoles