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The objective of this work is to demonstrate the utility of Lyapunovfunctions in control synthesis for the purpose of maintaining and stabilizing aspacecraft in a circular orbit around the L4 point in the circular restrictedthree body problem (CRTBP). Incorporating the requirements of a fixed radiusorbit and a desired angular momentum, a Lyapunov function is constructed andthe requisite analysis is performed to obtain a controller. Asymptoticstability is proved in a defined region around the L4 point using LaSalle'sprinciple.

Circular orbit spacecraft control at the L4 point using Lyapunov functions