  We study systems analogous to binary black holes with spin in order to gain
some insight into the origin and nature of "bobbing" motion and "kicks" that
occur in this system. Our basic tool is a general formalism for describing the
motion of extended test bodies in an external electromagnetic field in curved
spacetime and possibly subject to other forces. We first show that bobbing of
exactly the type as observed in numerical simulations of the binary black hole
system occurs in a simple system consisting of two spinning balls connected by
an elastic band in flat spacetime. This bobbing may be understood as arising
from the difference between a spinning body's "lab frame centroid" and its true
center of mass, and is purely "kinematical" in the sense that it will appear
regardless of the forces holding two spinning bodies in orbit. Next, we develop
precise rules for relating the motion of charged bodies in a stationary
external electromagnetic field in flat spacetime with the motion of bodies in a
weakly curved stationary spacetime. We then consider the system consisting of
two orbiting charges with magnetic dipole moment and spin at a level of
approximation corresponding to 1.5 post-Newtonian order. Here we find that
considerable amounts of momentum are exchanged between the bodies and the
electromagnetic field; however, the bodies store this momentum entirely as
"hidden" mechanical momentum, so that the interchange does not give rise to any
net bobbing. The net bobbing that does occur is due solely to the kinematical
spin effect, and we therefore argue that the net bobbing of the electromagnetic
binary is not associated with possible kicks. We believe that this conclusion
holds in the gravitational case as well.
