A key source of pointing jitter is due to reaction wheels (RWs) mass imbalance about the wheel spin axis. Although these effects are often characterized through experimentation in order to validate requirements, it is of interest to include jitter in a computer simulation of the spacecraft in the early stages of spacecraft development. An estimate of jitter amplitude may be found by modeling wheel unbalance torques as an external disturbance on the spacecraft In this case, reaction wheel mass imbalances are lumped into static and dynamic unbalance parameters, allowing jitter force and torque to be simply proportional to wheel speed squared. A physically realistic dynamic model may be obtained by defining mass imbalances in terms of a RW center of mass location and inertia tensor. The fully-coupled dynamic model allows momentum and energy validation of the system. This is often critical when modeling additional complex dynamical behavior such as flexible dynamics and fuel slosh. Furthermore, it is necessary to use the fully-coupled model in instances where the relative mass properties of the spacecraft with respect to the RWs cause the simplified jitter model to be inaccurate. This paper presents a generalized approach to reaction wheel imbalance modeling of a rigid hub with N reaction wheels. A discussion is included to convert from manufacturer specifications on RW unbalances to the introduced parameters. In addition, a back-substitution method is introduced to increase the computational efficiency of a computer simulation.
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