Data-Driven Discovery of Cislunar Transport Mechanisms (D3CTM)
Abstract
This proposal aims to develop innovative algorithms that combine semi-analytic and data-driven approaches to represent transport mechanisms in cislunar space. Insights from these methods are then leveraged to construct information-structures for representing and organizing trajectory characteristics and relating them to existing frameworks. The main thrust of the proposal is to leverage Hamilton-Jacobi (HJ) theory to simplify the representation of dynamics. The power of the HJ equations arises from the fact that the solution of a class of mechanics problems is reduced to the solution of a single partial differential equation, the HJ equation. Instead of directly providing the trajectories, the HJ solution provides a function called the action function that relates the initial state of the system to the total action (energy integral) accumulated along a specific trajectory. The primary task will be to develop a mathematical framework for solving the HJ equation in a computationally tractable form by utilizing advances in sparse-approximation theory to create parsimonious representations of action functions for defining coordinate transformations that capture relevant topological structures in cislunar transport. The proposal will also develop a comprehensive framework for local behavior of trajectories by posing the HJ equation in new innovative ways to extract dynamical structures in a user-friendly interpretable fashion for decision making. From a data-driven standpoint, this proposal will develop methodologies that circumvent the knowledge of an explicit Hamiltonian form by utilizing inherent information contained within the acceleration profiles of trajectories. Extensive validation of these developed tools is proposed within local domains near the Lagrange points and across multiple local domains, ensuring the robustness and applicability of the proposed framework.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2025
- Source ID
- FA95502510078
Entities
People
- Roshan Eapen
Organizations
- Air Force Office of Scientific Research
- Pennsylvania State University
- United States Air Force