The primary goals of the lab are associated with development of advanced algorithms for modeling, simulating, and analyzing the behavior of complex dynamic systems. Examples of such systems include, but are not limited to, spacecraft, bio-molecular systems, molecular dynamics of advanced materials, robotic systems, automotive applications, the human body, and manufacturing operations. These analysis and simulation tools emphasize the development of equations of motion, solution for state derivatives, temporal integration, determination of parameter sensitivities, and the nature of the computing system on which the simulation may be performed as a single unified problem. Consequently, these algorithms can obtain the desired accuracy, while requiring far fewer computational operations than their more traditional counterparts. This results in simulations which run much more quickly or, equally important, allow a level modeling and analysis that would otherwise be prohibitively expensive. This is often accomplished through the use of special low order algorithms, specialized integration schemes, and the intelligent exploitation of parallel computing.