Finding the 3 Axes of a Sakai Gyro

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In summary, the conversation discusses determining the three main axes of the moment of inertia for a Sakai gyro. The first axis is the upright because it is rotating around that axis, and the second axis is in the plane of the ring due to its symmetry. The third axis is perpendicular to the other two, and may not have a clear symmetry. Further calculations using discrete integrals are needed to accurately calculate the moment of inertia of the figure. A Google search provides a helpful resource on the topic.
  • #1
Icheb
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I have a Sakai gyro that looks like this:
http://img165.imageshack.us/img165/4556/sakainn4.gif

Now I have to find the three main axes of the moment of inertia by considering symmetries.

I put the two axes into the picture which I think I know. The first one would be the upright because it is rotating around that axis.
The second one would be the one in the plane of the ring because one half of the ring is symmetrical to other half.
But where would the third axis lie? I can't seem to find another symmetry. At first I just thought it's at a 90° angle to my second axis, but one half wouldn't be symmetrical to the other half.
 
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  • #2
Wow, that doesn't seem like an Introductory Physics question past the first axis. Would you like me to move it to the Advanced Physics homework forum?

And past that, it looks like you need to use a discrete integral to calculate the moment if inertia of that figure in the other axes. What are the integral equations that you would start with?
 
  • #3
You cannot always have three axes of symmetry. In fact you cannot always have two or even one. You have picked two reasonable axes based on the symmetries you have identified. Take the third on to be perpendicular to the other two. It is probably giving you too much information, but a google search on the Sakai top brings up a rather nice paper on the subject

http://www.e20.physik.tu-muenchen.de/~cucke/ftp/lectures/SAKAIEN.PDF
 
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1. How do you find the 3 axes of a Sakai Gyro?

To find the 3 axes of a Sakai Gyro, you can use a gyroscope sensor or a compass. The gyroscope sensor measures the rate of rotation around each axis, while the compass can determine the direction of the earth's magnetic field. By combining the data from these two instruments, you can determine the 3 axes of the Sakai Gyro.

2. What is the purpose of finding the 3 axes of a Sakai Gyro?

The 3 axes of a Sakai Gyro are essential for accurately measuring the orientation and rotation of an object. This information is crucial in various applications, such as navigation, robotics, and aerospace engineering. By knowing the 3 axes, you can track the movement and position of an object in 3D space.

3. What are the three axes of a Sakai Gyro?

The three axes of a Sakai Gyro are the roll axis, pitch axis, and yaw axis. The roll axis is the horizontal axis that goes through the center of the gyro, the pitch axis is the vertical axis that goes through the center, and the yaw axis is the axis that goes through the center perpendicular to both the roll and pitch axes.

4. How accurate is the data from finding the 3 axes of a Sakai Gyro?

The accuracy of the data from finding the 3 axes of a Sakai Gyro depends on various factors, such as the quality of the instruments used, external environmental factors, and the calibration of the sensors. Generally, modern gyroscopes and compasses are highly accurate and can provide precise data on the 3 axes of a Sakai Gyro.

5. Can the 3 axes of a Sakai Gyro change over time?

Yes, the 3 axes of a Sakai Gyro can change over time due to factors such as external disturbances, mechanical wear and tear, and calibration errors. It is essential to regularly calibrate and maintain the gyro to ensure accurate data on the 3 axes. Additionally, the axes can also change if the orientation or position of the object being measured changes.

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