In this report, we discuss the details of three recently developed techniques that provide significant enhancements to the molecular dynamics method and to the analysis of data. These techniques (called geometric statement functions, high resolution spectral methods, and computational neural networks) have been employed by us to study large molecular systems. Results are presented for applications to the structural and dynamical properties of crystalline polymers. Three categories are addressed: spectra and heat capacities, external interactions such as collisions and infrared laser-induced ablation, and conformational disorder and lamellar thickening in polymer crystals. The applicability and power of the new techniques is clearly established, yielding invaluable information on the atomistic details of crystalline polymer processes.