<p>This paper presents a variational integrator based on unit quaternions, designed to achieve a comprehensive simulation of the motion of plate-type broadband satellites under the influence of non-conservative forces and torques, encompassing translational, rotational, and vibrational dynamics. Initially, we derive a continuous coupled dynamic model that integrates the translational motion, attitude dynamics, and array vibrations of the satellite. This model thoroughly accounts for the time-varying characteristics of the satellite’s center of mass and their implications for the satellite’s inertia. Subsequently, we construct a Lie group-type variational integrator, grounded in the discrete Lagrange–d’Alembert principle, represented on the unit quaternion group. This integrator effectively balances the long-term structural stability of the system with the preservation of geometric properties throughout the computational process. Furthermore, we propose a universal iterative algorithm to enhance both the computational efficiency and accuracy concerning the implicit equations in the Hamiltonian form of the discrete dynamic equations. Finally, we compare numerical examples derived from the “Longjiang-3” satellite with results obtained using the ODE45 integrator. The numerical simulation results substantiate the effectiveness and superiority of both the proposed integrator and the iterative algorithm. In terms of energy and momentum variations, this integration scheme exhibits excellent symplectic behavior and demonstrates ideal conservation characteristics for both momentum and energy, thereby ensuring long-term stability in accurately simulating the dynamics of planar satellites. This work provides a theoretical foundation and practical framework for future research on satellite dynamics.</p>