The Poincare equations, also known as Lagrange's equations in quasi coordinates, are revisited with special attention focused on a diagonal form. The diagonal form stems from a special choice of quasi velocities that were first introduced by Georg Hamel nearly a century ago. The form has been largely ignored because the quasi velocities create so-called Hamel coefficients that appear in the governing equations and are based on the partial derivative of the mass matrix factorization. Consequently, closed-form expressions for the Hamel coefficients can be difficult to obtain and relying on finite-dimensional, numerical methods are unattractive. In this thesis we use a newly developed operator overloading technique to automatically generate the Hamel coefficients through exact partial differentiation together with numerical evaluation. The equations can then be numerically integrated for system simulation. These special Poincare equations are called the Hamel Form and their usefulness in dynamic modeling and control is investigated. Coordinated control algorithms for an automatic retargeting system are developed in an attempt to protect an area against direct assaults. The scenario is for a few weapon systems to suddenly be faced with many hostile targets appearing together. The weapon systems must decide which weapon system will attack which target and in whatever order deemed sufficient to defend the protected area. This must be performed in a real-time environment, where every second is crucial. Four different control methods in this thesis are developed. They are tested against each other in computer simulations to determine the survivability and thought process of the control algorithms. An auction based control algorithm finding targets of opportunity achieved the best results.

The main objective of this work is to demonstrate some new computational methods for estimation, optimization and modeling of dynamical systems that use automatic differentiation. Particular focus will be upon dynamical systems arising in Aerospace Engineering. Automatic differentiation is a recursive computational algorithm, which enables computation of analytically rigorous partial derivatives of any user-specified function. All associated computations occur, in the background without user intervention, as the name implies. The computational methods of this dissertation are enabled by a new automatic differentiation tool, OCEA (Object oriented Coordinate Embedding Method). OCEA has been recently developed and makes possible efficient computation and evaluation of partial derivatives with minimal user coding. The key results in this dissertation details the use of OCEA through a number of computational studies in estimation and dynamical modeling. Several prototype problems are studied in order to evaluate judicious ways to use OCEA. Additionally, new solution methods are introduced in order to ascertain the extended capability of this new computational tool. Computational tradeoffs are studied in detail by looking at a number of different applications in the areas of estimation, dynamical system modeling, and validation of solution accuracy for complex dynamical systems. The results of these computational studies provide new insights and indicate the future potential of OCEA in its further development.