The transfer is studied in the context of the classical Circular Restricted Three-Body Problem. The initial state is on a geosinchronous orbit and the terminal state is the L4 triangular Lagrangian point. The use of controllable acceleration engine by minimization of a time integral of the squared engine acceleration, the optimization problem is separated into two sub-problems: dynamical and parametric ones. Initial mass to constant output power ratio variation is mainly studied, depending on the transfer duration and initial thrust acceleration for fixed power jet (specific impulse is within the limits of the VASIMR magneto-plasma engine). The Two Point Boundary Value Problem is solved when the startup speed is circular or when the initial thrust acceleration is given. Time variation of the obtained state and control variables is represented relative to Earth in geocentric equatorial inertial system.
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