This paper presents a Lagrangian formulation for studying the dynamics and control of the Space Station based Mobile Servicing System (MSS) for a particular case of in-plane libration and maneuvers. The simplified case is purposely considered to focus on the effects of structural and joint flexibilities of the MSS on the complex interactions between the station and manipulator dynamics during slewing and translational maneuvers. The response results suggest that under critical combinations of parameters, the system can become unstable. During maneuvers, the deflection of the MSS can become excessive, leading to payload positioning error and the librational disturbance can also be significant. A linear quadratic regular is designed to simultaneously control the deflection of the manipulator and maintain the station at its operating configuration.