How Can I Decompose a 3x3 Rotation Matrix into a Product of 3 Rotations?

Thread starter Cristi-Tota
Start date Jul 3, 2005
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Decomposition Rotation

AI Thread Summary

To decompose a 3x3 rotation matrix R into a product of three rotations, the angles a, b, and c need to be determined for known unit vectors v1, v2, and v3. The feasibility of this decomposition is debated, with some suggesting that a general solution may not exist. Reference to Euler angles is recommended for further understanding of rotation representations. The discussion highlights the complexity of rotation matrix decomposition in three-dimensional space. Ultimately, the problem remains challenging and may require specific conditions for a solution.

Jul 3, 2005

Cristi-Tota

Hi,

How can I decompose a 3x3 rotation matrix R, into a form:

R = rot(v3,c) X rot(v2,b) X rot(v1,a)

where v1,v2,v3 are known unit length axes (with angles a,b,c unknowns)?

Thank you,
Cristian

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Jul 3, 2005

Timbuqtu

I don't think it can be solved generally. Have a look at:

http://mathworld.wolfram.com/EulerAngles.html

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