Application of Costate Mapping for Enforcing Classical Orbital Elements Boundary Conditions in Orbit Transfer Maneuvers

In astrodynamics and space flight mechanics problems, it is known that the choice of coordinates (and/or elements) has a significant influence on the convergence performance of the Hamiltonian/indirect boundary-value problems (HBVPs). It is oftentimes required to enforce the orbit-departure (or orbit-insertion) boundary conditions in terms of the classical orbital elements (COEs), which are more intuitive compared to the modified equinoctial elements (MEEs). In orbit design trade studies, it is quite common to seek an answer to the following question: What is the best orbit geometry to which a spacecraft can be transferred? We propose an easy-to-implement approach to enforcing orbit-departure/insertion transversality conditions using the costate mapping theory. This approach allows practitioners to formulate HBVPs using the set of MEEs (which is advantageous from a computational performance point of view) while enforcing the boundary conditions using the more intuitive COEs. Application of the method is demonstrated for generating minimum-fuel low-thrust trajectories between geocentric elliptical and near-circular orbits.