Finding Rotational matrix from axis-angle representation

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SUMMARY

The discussion focuses on deriving the rotational matrix R from an axis-angle representation, specifically using the axis vector u = (-1, -1, -1) and an angle of π/6. The user expresses uncertainty about their calculations and seeks assistance in verifying their results. Key insights include the importance of applying the rotational matrix to both the axis vector and a perpendicular vector to confirm correctness.

PREREQUISITES
  • Understanding of rotational matrices in 3D space
  • Familiarity with axis-angle representation of rotations
  • Knowledge of trigonometric functions for angle calculations
  • Basic linear algebra concepts, including vector operations
NEXT STEPS
  • Study the derivation of the Rodrigues' rotation formula
  • Learn how to apply rotational matrices to vectors in 3D
  • Explore the properties of orthogonal matrices and their applications
  • Investigate the implications of the right-hand rule in 3D rotations
USEFUL FOR

Students in physics or engineering, mathematicians working with 3D transformations, and anyone interested in computer graphics or robotics involving rotational dynamics.

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Homework Statement


Given an axis vector u=（-1, -1, -1) , find the rotational matrix R corresponding to an angle of pi/6 using the right hand rule. Then find R(x), where x = (1,0,-1)

Homework Equations


I found the relevant equation on wikipedia (see attachment)

The Attempt at a Solution


I feel that I'm doing something wrong but I don't know what; I think I performed the calculations correctly.
upload_2014-12-3_5-9-50.png
upload_2014-12-3_5-10-6.png
upload_2014-12-3_5-9-57.png

Please help?http://blob:https%3A//www.physicsforums.com/99c786ac-ed37-4fb2-8cd5-0d1ea0a3afb5
 

Attachments

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    Capture.PNG
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  • upload_2014-12-3_5-9-14.png
    upload_2014-12-3_5-9-14.png
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  • upload_2014-12-3_5-9-6.png
    upload_2014-12-3_5-9-6.png
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What makes you think something went wrong?
Have you tried testing it, i.e. by applying R to u, or to a vector perpendicular to u, and see if you get the right result?
 

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