1. Testing reaction wheel configurations via the generalized inverse. (a) Take a four-wheel pyramid configuration of...

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1. Testing reaction wheel configurations via the generalized inverse. (a) Take a four-wheel pyramid configuration of reaction wheels in the body-system as shown in class. Assume you want to have a fully symmetric configuration, where the wheel is at a distance of 10cm from the z-axis of the spacecraft. Show all intermediate steps, comment on your findings: (c) In the four-wheel pyramid, we are swapping the reaction wheels with control moment gyros (keeping the initial orientation of the rotation axes). For a CMG rotational speed of 6600 rpm, what is the orientation of the rotation axes to achieve the torque of LB = [1,2,3]Nm? (d) One often hears the term maximum load on a reaction wheel, what does that mean? Give anquantitative and qualitative answer. 1. Testing reaction wheel configurations via the generalized inverse. (a) Take a four-wheel pyramid configuration of reaction wheels in the body-system as shown in class. Assume you want to have a fully symmetric configuration, where the wheel is at a distance of 10cm from the z-axis of the spacecraft. Show all intermediate steps, comment on your findings: (c) In the four-wheel pyramid, we are swapping the reaction wheels with control moment gyros (keeping the initial orientation of the rotation axes). For a CMG rotational speed of 6600 rpm, what is the orientation of the rotation axes to achieve the torque of LB = [1,2,3]Nm? (d) One often hears the term maximum load on a reaction wheel, what does that mean? Give anquantitative and qualitative answer.