What Determines the Order of Rotations for a Gyro?

In summary, the spinning top needs some type of gimbal/support to keep it from rotating in other directions. The gimbals shown in the second picture are there to prevent the top from spinning out of control.
  • #1
Trying2Learn
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TL;DR Summary
This could be another idiotic question (let's hedge our bets and say it is). Still, regardless of Tait or Euler angles, what is the order of applying the rotations?
This could be a whole lot of nothing... however...

Here are two figures used in gyroscopic analyses.
Guidance.PNG
Gyro.PNG


  • On the left, is a model for an inertial guidance system on an airplane. As the airplane precesses (about the vertical 3-axis), and as the disk spins about the local 2-axis, there is an induced nuation, restricted by the springs, to measure the direction of the plane.
    • To model the system on the LEFT, I use the Tait angles in order: 3-axis, 1-axis, 2-axis. I can do this, and it all works out.
  • On the right, is a standard Cardan Gyroscope
    • To model the system on the RIGHT, I use the Euler angles in order: 3-axis, 1-axis, 3-axis. I can do this, and it all works out.
So far, so good, I understand.

Now suppose I remove all the structures/gimbals that "inform" me (or guide me) in the order of rotations? Suppose I delete everythig except the disk mass itself and leave it hanging in space.

What, in these stripped-down problems "informs" me of the order in which I apply the rotations?
Or, is the supporting structure itself, the thing that informs me? (I think this is true)

Thus, for the one on the RIGHT, why could I not model it in THIS order?
(It is still a 3, 1 3 Euler angle family)
  1. Spin of disk about 3-axis
  2. Nutation of disk about 1-axis
  3. Precession of disk about the local 3-axis

If I analyzed this in the order I just wrote, then, after the nutation, there is no remaining vertical axis about which to "precess" (so maybe that is the issue)

If I do it "correctly" and precessed, then nutated, there does remain the body disk axis about which to spin.

What is it about the stripped down disk, that in both figures, the SPIN is to the LAST of the rotations applied?
 
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  • #2
The spinning of a body at high angular velocity is the source of any precession; therefore, it must be first.
That fast spinning of a mass induces an angular momentum vector, which resists any change to its spatial orientation.

If an external moment applied on the spinning body forces a modification of that spatial orientation, a reactive moment appears and an additional rotation in a different direction is induced by that external moment.

The function of the gimbals shown in the second picture Is to isolate the spinning (at high rpm's) disc from any external moment, so it remains rotating in the same exact spatial orientation.

Please, see:
http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html#rvec4
 

Related to What Determines the Order of Rotations for a Gyro?

1. What is the purpose of the order of rotations for a gyro?

The order of rotations for a gyro is important because it determines the direction in which the gyro will rotate and the resulting motion of the object it is attached to. It also ensures that the gyro is stable and able to maintain its orientation in space.

2. What is the correct order of rotations for a gyro?

The correct order of rotations for a gyro is roll, pitch, and yaw. This means that the gyro will first rotate around its roll axis, then its pitch axis, and finally its yaw axis.

3. How does the order of rotations affect the accuracy of a gyro?

The order of rotations can greatly affect the accuracy of a gyro. If the order is incorrect, the gyro will not accurately measure the rotation of the object it is attached to. This can result in errors and incorrect readings.

4. Can the order of rotations for a gyro be changed?

Yes, the order of rotations for a gyro can be changed depending on the application. However, it is important to ensure that the order is correctly configured for the specific use case in order to obtain accurate results.

5. How do I determine the correct order of rotations for a gyro?

The correct order of rotations for a gyro can be determined by considering the axes of rotation of the object it is attached to and the desired orientation of the gyro. It is also important to consult the manufacturer's instructions for specific guidance on the correct order of rotations.

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