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!

Rotational symmetry

  1. Jun 6, 2009 #1
    I've been following along with Lenny Susskinds lectures on modern classical mechanics on youtube.

    at 34:30 he writes a few translation formulas on the board:
    delta X = - epsilon Y
    delta Y = epsilon X

    It's not obvious to me why these equations are true. I can't seem to find a derivation anywhere, nor can I work one out myself. Any help?
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Jul 9, 2009 #2
    I haven't watched the video, but if you perform a http://mathworld.wolfram.com/RotationMatrix.html" [Broken] by an angle [itex]\theta[/itex] about the [itex]z[/itex] axis on the vector [itex] {\bf r} = \left(x,y,z\right) [/itex], you get [itex] r' = r + \Delta r = \left(\cos \theta x - \sin \theta y, \sin \theta x + \cos \theta y ,z\right) [/itex]. For [itex]\theta = \epsilon[/itex] infinitesimal, this becomes [itex] r' = r + \delta r = \left(x - \epsilon y, \epsilon x + y ,z\right) = r + \left(- \epsilon y, \epsilon x ,0\right) [/itex], so that [itex] \delta x = - \epsilon y[/itex] and [itex] \delta y = - \epsilon x[/itex].
    Last edited by a moderator: May 4, 2017
  4. Jul 14, 2009 #3
    thanks, that's what I was looking for.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook