  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.
