Finding Rotational matrix from axis-angle representation

In summary, the conversation discusses finding a rotational matrix R for an angle of pi/6 using the right hand rule, with given axis vector u=(-1,-1,-1). The equation from wikipedia is referenced and it is noted that the calculations may have been performed correctly, but further testing is needed to confirm the accuracy of the results.
  • #1
fakecop
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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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  • upload_2014-12-3_5-9-6.png
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  • #2
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?
 

Related to Finding Rotational matrix from axis-angle representation

1. What is a rotational matrix and why is it important?

A rotational matrix is a mathematical representation of a rotation in three-dimensional space. It is important because it allows us to describe and manipulate rotations in a precise and efficient manner, making it useful in many fields such as physics, computer graphics, and engineering.

2. What is an axis-angle representation and how is it related to rotational matrices?

An axis-angle representation is a way of representing a rotation using an axis and an angle of rotation around that axis. This representation is closely related to rotational matrices, as the axis and angle can be used to calculate the elements of a rotational matrix that describes the same rotation.

3. How do you find a rotational matrix from an axis-angle representation?

To find a rotational matrix from an axis-angle representation, you can use the Rodriguez formula. This involves constructing a skew-symmetric matrix from the axis vector and then using this matrix to calculate the desired rotational matrix. Alternatively, you can use trigonometric functions to directly compute the elements of the rotational matrix.

4. Can all rotations be represented by a rotational matrix?

No, not all rotations can be represented by a rotational matrix. Only rotations in three-dimensional space can be described by a 3x3 rotational matrix. Rotations in higher dimensions require a different mathematical representation.

5. Are there any limitations or drawbacks to using rotational matrices?

Like any mathematical representation, rotational matrices have limitations and drawbacks. One limitation is that they can only describe rigid rotations, meaning that the distance between points remains the same after the rotation. Additionally, they can become computationally expensive for complex rotations, and they may not be suitable for describing continuous rotational movements.

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