A Why are Euler's angles picked exactly that way?

  • A
  • Thread starter Thread starter illidan4426
  • Start date Start date
  • Tags Tags
    Angles
AI Thread Summary
Euler's angles are defined by a specific sequence of rotations around the axes: first around the z-axis, then the x-axis, and finally the z-axis again. This particular order is crucial because it leads to a unique representation of orientation in three-dimensional space. Alternative sequences, such as rotating around the x-axis first, would result in different transformation equations and potentially ambiguous orientations. The choice of convention in parametrizing rotations is essential for consistency in applications like robotics and aerospace. Understanding these conventions is key to accurately describing motion and orientation in 3D systems.
illidan4426
Messages
1
Reaction score
0
TL;DR Summary
I'm wondering why exactly those angles are picked to describe the orientation of the rotating body.
So the Euler's angles are described like this:
xyz-x'y'z' (first rotation around z axis)
x'y'z'-x''y''z'' (second rotation around x')
x''y''z''-XYZ (third rotation around z'')
So I've been thought it goes like this, now I'm wondering why? Why exactly these angles and why this order? Why can't it go like this for example:
xyz-x'y'z' (rotate around x)
x'y'z'-x''y''z'' (rotate around y')
x''y''z''-XYZ (rotate around z'')
Can the motion be described this way? The equations of transformation of xyz-XYZ would be different for sure.
 
Last edited:
Physics news on Phys.org
There are all kinds of conventions around to parametrize the rotations. The Euler angles are just the most often used ones.
 
Reply
  • Like
Likes Vanadium 50 and topsquark

Thread 'The Effect of Linear and Rotational Motion on Measured Weight'

Consider an extremely long and perfectly calibrated scale. A car with a mass of 1000 kg is placed on it, and the scale registers this weight accurately. Now, suppose the car begins to move, reaching very high speeds. Neglecting air resistance and rolling friction, if the car attains, for example, a velocity of 500 km/h, will the scale still indicate a weight corresponding to 1000 kg, or will the measured value decrease as a result of the motion? In a second scenario, imagine a person with a...
View full post »

Thread 'Simple thought experiment with Stefan-Boltzmann law: energy'

Dear all, in an encounter of an infamous claim by Gerlich and Tscheuschner that the Greenhouse effect is inconsistent with the 2nd law of thermodynamics I came to a simple thought experiment which I wanted to share with you to check my understanding and brush up my knowledge. The thought experiment I tried to calculate through is as follows. I have a sphere (1) with radius ##r##, acting like a black body at a temperature of exactly ##T_1 = 500 K##. With Stefan-Boltzmann you can calculate...
View full post »
Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »

Similar threads

A Euler vs. Tait (steady precession vs... what?)
Replies
1
Views
1K
I Rotating plate thrown parallel to ground
Replies
2
Views
1K
I Understanding 3D Coordinate Rotations with Euler Angles
Replies
2
Views
2K
A Electric and magnetic field lines in a plane wave of finite extent
Replies
1
Views
1K
A Corresponding case of steady precession but for Tait-Bryan angles
Replies
1
Views
1K
I How can Euler angles be visualized using a polar plot?
Replies
1
Views
2K
3D Coordinate transformation and Euler Angles
Replies
4
Views
3K
A Are Tait and Euler angles a complete parametrization of 3D space?
Replies
7
Views
2K
A Can the orientation of a body be defined by Euler angles?
Replies
18
Views
2K
Angle between two orthogonal coordinate systems
Replies
16
Views
9K

Hot Threads

Recent Insights

Back
Top