MATLAB-Based Orbital Coordinate System Transformation Program

This program provides comprehensive functionality for transforming between coordinate systems used in orbital mechanics. The core algorithm implements the Poincaré vector method, a vector-based approach for celestial orbit description, which facilitates conversion between geocentric rectangular coordinates (x, y, z) and orbital parameters. The implementation includes specialized functions that handle the mathematical transformations using matrix operations and vector calculus. Additionally, the program incorporates orbital elements processing, utilizing a set of six parameters (semi-major axis, eccentricity, inclination, right ascension, argument of perigee, mean anomaly) to describe orbital shapes. The conversion routines employ Keplerian equations and coordinate rotation matrices to ensure accurate transformations between different representations. Key computational features include: - Vector transformation functions using 3D rotation matrices - Kepler's equation solvers for mean anomaly calculations - Coordinate system transformation algorithms with error checking - Visualization modules for plotting orbital trajectories in 3D space - Auxiliary functions for orbital parameter calculations (period, velocity, etc.) The program architecture includes modular functions for each transformation type, with input validation and unit consistency checks. Visualization capabilities generate 2D and 3D plots of orbital paths using MATLAB's graphics functions, while computational modules provide derived parameters like orbital period and velocity vectors.