Computational aspects of multilevel trajectory optimization

This paper presents new computational results in multilevel trajectory optimization. The original formulation of trajectory decomposition is extended and applied to a difficult multiple arc trajectory example, the low thrust interplanetary swingby problem. A numerical solution is obtained for this trajectory which is characterized by nonlinear, time variant differential equations and interior boundaries and discontinuities. The time domain decomposition of the trajectory is made at the boundaries between arc segments. A three level optimization hierarchy is employed to transform the first feasible trajectory iterate into a final solution trajectory. This example is characteristic of a large class of interplanetary swingby problems which defy solution by conventional computational methods because of multiple discontinuities, constraints, and severe numerical sensitivities. The multilevel approach appears to be effective in obtaining a solution to problems of this type when other more conventional methods are unsatisfactory

Interference, reduced action, and trajectories

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function's trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.Comment: 12 pages text, 5 figures. Typos corrected. Author's final submission. A companion paper to "Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment", quant-ph/0605121. Keywords: interference, nonlocality, trajectory representation, entanglement, dwell time, determinis