In this paper, the motion of a smart rigid-flexible satellite by considering large deformations for its flexible appendages in general planar motion is modeled. Therefore, the satellite can experience translational and rotational motions also its flexible appendages can vibrate arbitrarily in the motion plane. Two control forces perpendicular to each other and one control torque are responsible for controlling the motion of the satellite on the desired trajectories. Also, piezoelectric actuators and sensors suppress vibrations and estimate the transverse displacement of the satellite's flexible appendages, respectively. The coupled ordinary-partial differential equations of motion, equations of the sensors, and boundary conditions of the system are obtained using extended Hamilton's principle. Then, these equations are discretized using the Galerkin method. The discretized equations of motion are a set of coupled nonlinear ordinary differential equations due to the consideration of the large rotation angle of the satellite and large deformations for its flexible appendages. Adaptive super-twisting global nonlinear sliding mode controller is designed to satisfy the control objectives including position and attitude control, as well as suppressing vibrations of the flexible appendages in the presence of uncertainties and external disturbances. Eventually, numerical simulations are presented to illustrate the effectiveness of the proposed controller.