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This work shows that a class of astrodynamics problems subject to missionconstraints can be efficiently solved using the Theory of FunctionalConnections (TFC) mathematical framework by a specific change of coordinates.In these problems, the constraints are initially written in non-linear andcoupled mathematical forms using classical rectangular coordinates. Thesymmetries of the constrained problem are used to select a new system ofcoordinates that transforms the non-linear constraints into linear. This changeof coordinates is also used to isolate the components of the constraints. Thisway the TFC technique can be used to solve the ordinary differential equationsgoverning orbit transfer problems subject to mission constraints. Specifically,this paper shows how to apply the change of coordinates method to the perturbedHohmann-type and the one-tangent burn transfer problems.

Orbit transfer using Theory of Functional Connections via change of variables