Euler angles of rotation about x=y=z

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SUMMARY

The Euler angles of rotation about the line x=y=z for an angle of 2π/3 radians can be determined using the rotation matrix Rα,β,γ and a transformation matrix Q. The relationship Rα,β,γv = Qv must be solved for the angles α, β, and γ. Additionally, converting from quaternion representation to Euler angles may provide the necessary solution. For further details, refer to the Wikipedia page on conversion between quaternions and Euler angles.

PREREQUISITES
  • Understanding of Euler angles and their applications in 3D rotations
  • Familiarity with rotation matrices and their properties
  • Knowledge of quaternions and their relationship to Euler angles
  • Basic linear algebra concepts, particularly vector transformations in R3
NEXT STEPS
  • Study the derivation and application of rotation matrices in 3D space
  • Learn about quaternion representation and its advantages over Euler angles
  • Explore the mathematical properties of the transformation matrix Q
  • Investigate practical applications of Euler angles in computer graphics and robotics
USEFUL FOR

Mathematicians, computer graphics developers, and robotics engineers who require a solid understanding of 3D rotations and transformations.

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What would be the euler angles of rotation 2pi/3 about the line x=y=z? If something were in the xy plane and it underwent that rotation, would it end up in the yz plane?
 
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I am not totally sure about this but as a starting point you could consider the rotation matrix with Euler angles R_{\alpha,\beta,\gamma}, and a transformation matrix Q which rotates around the axis x=y=z of 2\pi / 3 radians. Then for any vector v \in \mathcal{R}^3, you essentially want to solve for \alpha,\beta,\gamma the following system:

R_{\alpha,\beta,\gamma}v=Qv

Also, try to take a look here: http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles because you might already find the solution you were looking for. I suspect you are essentially looking for a conversion from quaternion representation to Euler angles.
Hope it helped.
 

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