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JSPAM models galaxy collisions using a restricted n-body approach to speed up computation. Instead of using a softened point-mass potential, the software supports a modified version of the three component potential created by Hernquist (1994, ApJS 86, 389). Although spherically symmetric gravitationally potentials and a Gaussian model for the bulge are used to increase computational efficiency, the potential mimics that of a fully consistent n-body model of a galaxy. Dynamical friction has been implemented in the code to improve the accuracy of close approaches between galaxies. Simulations using this code using thousands of particles over the typical interaction times of a galaxy interaction take a few seconds on modern desktop workstations, making it ideal for rapidly prototyping the dynamics of colliding galaxies. Extensive testing of the code has shown that it produces nearly identical tidal features to those from hierarchical tree codes such as Gadget but using a fraction of the computational resources. This code was used in the Galaxy Zoo: Mergers project and is very well suited for automated fitting of galaxy mergers with automated pattern fitting approaches such as genetic algorithms. Java and Fortran versions of the code are available.