Due to the fact that the spacecraft equations of motion are given in inertial coordinates (SCS), while the spacecraft boundary conditions are given in relative-to-planet coordinates (ECS) or (MCS), coordinate transformations are needed to pass from one system to another at the terminal points of the outgoing and return trips. The transformations are given below.
ECS-to-SCS Transformation. For the outgoing trip, this transformation is to be employed to convert spacecraft conditions at the departure from LEO (time t = 0) from relative-to-Earth coordinates to inertial coordinates. In Cartesian coordinates,
SCS-to-MCS Transformation. For the outgoing trip, this transformation is to be employed to convert spacecraft conditions at the arrival to LMO (time t = ?) from inertial coordinates to relative-to-Mars coordinates. In Cartesian coordinates,
MCS-to-SCS Transformation. For the return trip, this transformation is to be employed to convert spacecraft conditions at the departure from LMO (time t = 0) from relative-to-Mars coordinates to inertial coordinates. In Cartesian coordinates,
SCS-to-ECS Transformation. For the return trip, this transformation is to be employed to convert spacecraft conditions at the arrival to LEO (time t = ?) from inertial coordinates to relative-to-Earth coordinates. In Cartesian coordinates,
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