We present Reactive Vega, a system architecture that provides the first robust and comprehensive treatment of declarative visual and interaction design for data visualization. Starting from a single declarative specification, Reactive Vega constructs a dataflow graph in which input data, scene graph elements, and interaction events are all treated as first-class streaming data sources. To support expressive interactive visualizations that may involve time-varying scalar, relational, or hierarchical data, Reactive Vega's dataflow graph can dynamically re-write itself at runtime by extending or pruning branches in a data-driven fashion. We discuss both compile- and run-time optimizations applied within Reactive Vega, and share the results of benchmark studies that indicate superior interactive performance to both D3 and the original, non-reactive Vega system.

The low-thrust spacecraft trajectory problem can be reduced to only a few parameters using calculus of variations and the well-known primer vector theory. This low dimensionality combined with the extraordinary speed of modern computers allows for rapid exploration of the parameter space and invites opportunities for global optimization. Accordingly, a general low-thrust trade analysis tool is developed based on a global search for local indirect method solutions. An efficient propagator is implemented with an implicit "bang-bang" thrusting structure that accommodates an a priori unknown number of switching times. An extension to the standard adjoint control transformation is introduced that provides additional physical insight and control over the anticipated evolution of the thrust profile. The uniformly random search enjoys a perfect linear speedup for parallel implementation. The method is applied specifically on multirevolution transfers in the Jupiter-Europa and Earth-moon restricted three body problems. In both cases, thousands of solutions are found in a single parallel run. The result is a global front of Pareto optimal solutions across the competing objectives of flight time and final mass.

The computations of the high-order partial derivatives in a given problem are often cumbersome or not accurate. To combat such shortcomings, a new method for calculating exact high-order sensitivities using multicomplex numbers is presented. Inspired by the recent complex step method that is only valid for firstorder sensitivities, the new multicomplex approach is valid to arbitrary order. The mathematical theory behind this approach is revealed, and an efficient procedure for the automatic implementation of the method is described. Several applications are presented to validate and demonstrate the accuracy and efficiency of the algorithm. The results are compared to conventional approaches such as finite differencing, the complex step method, and two separate automatic differentiation tools. The multicomplex method performs favorably in the preliminary comparisons and is therefore expected to be useful for a variety of algorithms that exploit higher order derivatives.

A global grid search is performed to find axi-and doubly-symmetric periodic orbits in the restricted three-body problem using the dimensioned parameters associated with the JupiterEuropa system. Local differential correctors are applied to regions of the initial condition phase space that appear to be near solutions. A three-dimensional initial condition mesh with billions of nodes is evaluated, and over 600,000 periodic solutions are identified. Families of direct and retrograde solutions, both new and previously published, are identified and discussed. Stability is analyzed for each solution and general regions of stability are noted. Of the most promising results is the observation and characterization of a large class of stable yet highly-inclined direct orbits. Finally, all of the solutions and associated properties are archived. The resulting database is a practical reference for preliminary design of missions to Europa.

A new algorithm is presented to solve constrained nonlinear optimal control problems, with an emphasis on highly nonlinear dynamical systems. The algorithm, called HDDP, is a hybrid variant of differential dynamic programming, a proven second-order technique that relies on Bellman's Principle of Optimality and successive minimization of quadratic approximations. The new hybrid method incorporates nonlinear mathematical programming techniques to increase efficiency: quadratic programming subproblems are solved via trust region and range-space active set methods, an augmented Lagrangian cost function is utilized, and a multiphase structure is implemented. In addition, the algorithm decouples the optimization from the dynamics using first-and second-order state transition matrices. A comprehensive theoretical description of the algorithm is provided in this first part of the two paper series. Practical implementation and numerical evaluation of the algorithm is presented in Part 2.