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!

A Generators of Lie Groups and Angular Velocity

  1. Jan 29, 2017 #1
    I envision the three fundamental rotation matrices: R (where I use R for Ryz, Rzx, Rxy)

    I note that if I take (dR/dt * R-transpose) I get a skew-symmetric angular velocity matrix.
    (I understand how I obtain this equation... that is not the issue.)

    Now I am making the leap to learning about Lie Algebras and Lie Groups

    And I understand that any Rotation matrix can be represented with the exponential map
    And with the exponential map, the generator of the map happens to have a form that is skew symmetric and (aside from the coefficients) of the same form as the angular velocity matrix.

    Of course. A rotatoin matrix is a change. The skew symmetric angular velocity matrix is a RATE of change.
    How is it possible for these to related to each other through an exponential map that does not involve TIME.
    Last edited by a moderator: Jan 29, 2017
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted