The attitude and position control problem for two-body system in two-dimensional inertial space is discussed. Three thrusters are equipped with one side of two-body. This two-body system contains control input which is constrained to be non-negative. The constraint as unilateral control input provides a challenging research area of increasing interest in both application and theory. This interesting problem is announced at 24th The International Symposium on Space Technology. In this paper, this important class of underactuated mechanical control system is examined and problems in both nonlinear controllability and nonlinear control design are addressed.