Three-Body Coulomb Problem
Closely related to the three-body gravitational problem is the classical, nonrelativistic three-body Coulomb problem, in which the forces between the bodies can be either attractive or repulsive, depending on the signs of the charges. Applications include studies of the quantum mechanical limit of helium-like two-electron ions and collisions between atoms and charged particles.
The equation of motion is
where is the acceleration of the body, , are the electric charges, is the mass, and is the vector connecting the masses and .
 J. C. Sprott, Elegant Chaos: Algebraically Simple Chaotic Flows, Singapore: World Scientific, 2010 pp. 121–123. www.worldscientific.com/worldscibooks/10.1142/7183# t=aboutBook.