Coffey, ShannonDeprit, AndréDeprit, EitenneHealy, LiamMiller, BruceUsing the main problem of artificial satellite theory as an illustration, we review several developments which have had a significant impact on research in nonlinear dynamics. On the mathematical front, we point to the theory of Lie transformations; in the area of computational software, we explain how massively data parallel machines open the way for symbolic solution of large problems. Finally, we show how color graphics assist in the qualitative analysis of dynamical systems.en-USsatellite orbitsvisualizationphase spaceHamiltonian systemsparallel processingcomputer algebraHamiltonian normalizationBook chapter