Position and attitude of under-actuated satellites is difficult to control because of their unique system called the non-holonomic systems. One of the ways to control the non-holonomic system is to use the holonomy that appears when the periodic input is given to the non-holonomic systems. In this study, the attitude and position of underactuated satellite is controlled using the holonomy. The satellite used in this study is simplified 2-dimensional model with only thrusters to change positions and attitude angle. Various pattern of periodic input gives the different holonomy to the system. In this paper, the input patterns of the holonomy are examined by the numerical optimization to see the effectiveness of the control theory.