# Difference between gyroscope angular displacement and Euler angles

• ZekDe
In summary: So gyroscopes measure angular rates and then convert them to Euler angles. Euler angles are used to keep track of the orientation of the aircraft.
ZekDe
Hi guys, I'm trying to understand between gyroscope angular displacement and euler angles?
for example { Δx = Δx + h * Rx * SCx);} this is gyroscope output about anguler displacement.This value can be used to determine angle that
device created.Why we should euler angles to fly.(I know quaternions.I just try to understand the difference)

Gyroscopes on airplanes are usually hard-mounted on the frame and give you the rotation rates, not the total displacement. The rates are integrated external to the gyroscope hardware to keep track of the angles.
As an airplane rolls, pitches, and yaws, a particular gyroscope angular rate represents rotations in different directions. It is necessary to keep track of the airplane orientation to know how the gyroscope rates should be interpreted in Euler angles.

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What about DCM,firstly we need to convert body-frame to inertial-frame.What is the purpose?.it that how degree we got displacement according to inertial-frame?

There are a lot of coordinate systems used in an Inertial Navigation System (INS): INS mount, body-frame, locally-level, Earth-Centered-Earth-Fixed (ECEF), Latitude Longitude Altitude (LLA). And there is a reason for each one. For one thing, body-frame coordinates wouldn't tell the airplane which way gravity is pointing, which is important for interpreting the accelerometer measurements. For another thing, the rotation of the Earth shows up in modern gyro outputs, so it is necessary to know what direction that is into interpret the gyro readings. The mathematics of a modern INS is quite complicated. There are all sorts of Direction Cosine Matrices and integrals used. The long-term drift of the integrals is periodically corrected using fixes on known positions (these days, GPS inputs). The errors of the merged inputs are minimized using Kalman filters. So many of the inputs are communicated in different coordinate systems that DCMs are all over the place. I have not looked at it in detail, but this looks like a good simplified introduction (especially if you have access to MATLAB)

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Klystron and anorlunda
FactChecker
thank you for your interest,I thought about it and solved the massy information in my mind.Excatly that is what did you say.

## 1. What is the difference between gyroscope angular displacement and Euler angles?

Gyroscope angular displacement refers to the change in orientation of an object in three-dimensional space, while Euler angles are a set of three angles that describe the orientation of an object relative to a fixed coordinate system.

## 2. How are gyroscope angular displacement and Euler angles measured?

Gyroscope angular displacement is typically measured using a gyroscope sensor, which detects changes in rotational movement. Euler angles are measured using a variety of methods, such as using a protractor or a computer program.

## 3. Can gyroscope angular displacement and Euler angles be used interchangeably?

No, gyroscope angular displacement and Euler angles are not interchangeable. They represent different ways of describing an object's orientation in space and cannot be directly converted into one another.

## 4. In what situations would you use gyroscope angular displacement versus Euler angles?

Gyroscope angular displacement is commonly used in applications that require precise measurement of rotational movement, such as in navigation systems or robotics. Euler angles are often used in computer graphics and animation to represent the orientation of 3D objects.

## 5. Are there any limitations to using gyroscope angular displacement and Euler angles?

Yes, both measurements have limitations. Gyroscope angular displacement can be affected by external forces such as vibrations or magnetic fields, while Euler angles can experience gimbal lock, a situation where one of the angles becomes redundant and causes a loss of information about the object's orientation.

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