A model for a two degree of freedom coupled seeker with mass imbalance

Two degree of freedom seekers are used in many aerospace applications. When designing the control loops for such seekers a planar representation is usually adequate. However when the seeker is modeled in conjunction with an overall system concept, the coupled two degree of freedom equations must be used. In addition seekers are not perfectly balanced and they generally have a center of gravity (CG) offset relative to the gimbal rotation axes. The effects of this imbalance must be modeled to determine just how much CG offset can be allowed. The derivation of the equations of motion for a two degree of freedom coupled seeker with no crossproducts of inertia or mass imbalance has been presented by Cannon (1967). This paper extends this approach to the case of inertia coupling and mass imbalance. A block diagram is also presented representing the math flow diagrams from which the seeker math model may be developed.