Exactly integrable analogue of a one-dimensional gravitating system

Exchange symmetry in acceleration partitions the configuration space of an N particle one-dimensional gravitational system (OGS) into N! equivalent cells. We take advantage of the resulting small angular separation between the forces in neighboring cells to construct a related integrable version of the system that takes the form of a central force problem in N−1 dimensions. The properties of the latter, including the construction of trajectories and possible continuum limits, are developed. Dynamical simulation is employed to compare the two models. For some initial conditions, excellent agreement is observed.