1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Am I doing this right? Doesn't feel right. (find axis of rotation)

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data

    So here is the question:

    Matrix A corresponds to the linear transformation T obtained by first rotating a vector in R3 through angle ∏/3 about the z axis and then through angle ∏/4 about the x-axis. Find the parametric equation for the axis of rotation.

    2. Relevant equations



    3. The attempt at a solution

    Finding matrix A: First I write down the two standard rotations with the first one on the right and multiply them:

    5AEMj.jpg

    This gives me matrix A. I then take the result and subtract the 3x3 identity matrix (so Mat(A) - I3). I augment this by the 3x1 zero vector and rref. So the following is what I am rref-ing. (so I am solving this system (A-I)[w]=0, and the axis parallel to [w] is the axis of rotation)

    CQBb0.jpg

    But when I rref this, I get the following:

    W3=t where t is in the reals
    W2=-0.4142t
    W1=0.7174t

    This doesn't seem right to me.. so the parametric form of the axis of rotation is this:

    x=0.7174t
    y=-0.4142t
    z=t

    Thanks so much in advance!
     
  2. jcsd
  3. Mar 17, 2012 #2
    The rotation axis must be perpendicular to both the starting vector and the ending vector, how do you find such a vector that is perpendicular to both?
     
  4. Mar 18, 2012 #3
    I don't quite understand, what are the "starting" and "ending" vectors? Does that mean that my method above is wrong?

    I know that the cross product is how you find a vector that is perpendicular to two other vectors.
     
  5. Mar 18, 2012 #4
    I'm sorry for providing wrong information. Please ignore my last post.
    Regarding the problem. If you wrote down the rotation matrix correctly, you should get the right answer. The rotation axis is nothing but the eigenvector of the rotation matrix with eigenvalue 1, which, after I solved for it, is exactly [0.7174, -0.4142, 1]'. If you get a different answer, try to check your calculation. FYI, the rotation matrix I got was
    [0.5,-0.866,0
    0.6124,0.3536,-0.7071
    0.6124,0.3536,0.7071]
    Check your work.
     
    Last edited: Mar 18, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Am I doing this right? Doesn't feel right. (find axis of rotation)
  1. Am I doing this right? (Replies: 7)

  2. Am I doing it right? (Replies: 3)

  3. Am i doing this right (Replies: 4)

  4. Am I doing this right? (Replies: 1)

Loading...