We have investigated the synchronization and antisynchronization behaviour of two identical planar oscillation of a satellite in\r\nelliptic orbit evolving from different initial conditions using the active control technique based on the Lyapunov stability theory\r\nand the Routh-Hurwitz criteria. The designed controller, with our own choice of the coefficient matrix of the error dynamics that\r\nsatisfy the Lyapunov stability theory and the Routh-Hurwitz criteria, is found to be effective in the stabilization of the error states\r\nat the origin, thereby, achieving synchronization and antisynchronization between the states variables of two nonlinear dynamical\r\nsystems under consideration. The results are validated by numerical simulations using mathematica.
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