# Question 10.14: A satellite is in torque-free motion. A control moment gyro,...

A satellite is in torque-free motion. A control moment gyro, spinning at the constant rate \omega_{s}, is gimbaled about the spacecraft y and z axes, with φ = 0 and φ = 90° (cf. Figure 10.26 ). The spacecraft angular velocity is \omega=\omega_{z} \hat{ k }. If the spin axis of the gyro, initially along the x direction, is rotated around the y axis at the rate \dot{\theta}, what is the resulting angular acceleration of the spacecraft?

**"Step-by-Step Explanation"**refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.

Our explanations are based on the best information we have, but they may not always be right or fit every situation.

**blue check mark**means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.

Learn more on how we answer questions.

## Related Answered Questions

Question: 10.15

## Verified Answer:

Let us first determine whether we can stabilize th...

Question: 10.13

## Verified Answer:

Using Figure 10.26 as a guide, we set φ = 0 and φ ...

Question: 10.12

## Verified Answer:

The absolute angular velocity of the xyz frame is ...

Question: 10.11

## Verified Answer:

For n = 3, Equation 10.140 becomes
\left\{ ...

Question: 10.10

## Verified Answer:

In this case we have only one “reaction wheel,” na...

Question: 10.9

## Verified Answer:

The plate plays the role of the body of a spacecra...

Question: 10.8

## Verified Answer:

(a) From Equation 10.104,
K=1+\frac{C}{m R^...

Question: 10.7

## Verified Answer:

According to Figure 9.9c, the moments of inertia a...

Question: 10.6

## Verified Answer:

The data in (a) are for a major axis spinner. Subs...

Question: 10.5

## Verified Answer:

For the cylindrical shell A, we have
r_{B}=...