Application of the Theory of Functional Connections to the Perturbed Lambert's Problem

A numerical approach to solve the perturbed Lambert's problem is presented. The proposed technique uses the Theory of Functional Connections, which allows the derivation of a constrained functional that analytically satisfies the boundary values of Lambert's problem. The propagation model is devised in terms of three new variables to mainly avoid the orbital frequency oscillation of Cartesian coordinates. Examples are provided to quantify robustness, efficiency, and accuracy on Earth and Sun centered orbits with various shapes and orientations. Differential corrections and a robust Lambert solver are used to validate the proposed approach in various scenarios and to compare it in terms of speed and robustness. Perturbations due to Earth's oblateness, third-body, and Solar radiation pressure are introduced, showing the algorithm's flexibility. Multi-revolution solutions are obtained. Finally, a polynomial analysis is conducted to show the dependence of convergence time on polynomial type and degree.