A new symplectic N-body integrator is introduced, one designed to calculate the global 360degrees evolution of a self-gravitating planetary ring that is in orbit about an oblate planet. The great advantage of this approach is that the perturbing forces arise from smooth wires of ring matter rather than discreet particles, so there is very little gravitational scattering and so only a modest number of particles are needed to simulate, say, the scalloped edge of a resonantly confined ring or the propagation of spiral density waves. Cassini observations show that the B ring-edge has several free normal modes, which are long-lived disturbances of the ring-edge that are not driven by any known satellite resonances. These simulations also indicate that impulsive disturbances at a ring can excite long-lived normal modes, which suggests that an impact in the recent past by perhaps a cloud of cometary debris might have excited these disturbances, which are quite common to many of Saturn's sharp-edged rings.