Nodal Restoration of 6-DOF Flight Dynamics: A 5D A5 Lattice Approach to Turbulence Mitigation and Energy Efficiency

Title Dataset and Simulation Environment for Nodal Restoration of 6-DOF Flight Dynamics using the $A_5$ Root System Description This repository contains the supporting data, simulation source code, and mathematical derivations for the paper "Nodal Restoration of 6-DOF Flight Dynamics: A 5D $A_5$ Lattice Approach to Turbulence Mitigation and Energy Efficiency." Overview Traditional 6-DOF control systems (PID/LQR) are reactive and energy-intensive in stochastic environments. This dataset demonstrates the efficacy of the Patel-Ramanujan Nodal Law, which utilizes the 109-node $A_5$ weight lattice to anchor aircraft states to geometric stability points. By enforcing a zero-sum manifold ($\sum q_i = 0$), the law achieves "Static Torque Cancellation," resulting in a 94.3% reduction in attitude error and a 56.6% reduction in control effort. Contents JSBSim Configuration Files: XML-based Flight Control System (FCS) files implementing the $A_5$ projection matrix and table-lookup for nodal anchoring. $A_5$ Lattice Coordinates: A CSV file containing the pre-computed 109 nodal anchors derived from the $A_5$ root system, normalized for 6-DOF flight states. Simulation Results: Raw telemetry data (CSV) from 50 Monte Carlo runs comparing LQR and Nodal Restoration performance under Dryden turbulence. Analysis Scripts: Python/MATLAB scripts used to generate phase portraits (p vs $\phi$) and Integrated Control Effort (ICE) metrics. Keywords Flight Control, Geometric Control, $A_5$ Root System, JSBSim, Turbulence Mitigation, Energy Efficiency, Nodal Restoration, 6-DOF Dynamics. Usage Notes To reproduce the findings, the JSBSim FDM engine is required. The provided XML files should be placed in the /Systems/ directory of the generic transport aircraft model. The stability proof is provided in the accompanying PDF documentation.