
#1
Jun609, 04:16 AM

P: 11

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 http://www.youtube.com/watch?v=FZDy_Dccv4s 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? 



#2
Jul909, 11:46 PM

P: 4

I haven't watched the video, but if you perform a rotation by an angle [latex]\theta[/latex] about the [latex]z[/latex] axis on the vector [latex] {\bf r} = \left(x,y,z\right) [/latex], you get [latex] r' = r + \Delta r = \left(\cos \theta x  \sin \theta y, \sin \theta x + \cos \theta y ,z\right) [/latex]. For [latex]\theta = \epsilon[/latex] infinitesimal, this becomes [latex] r' = r + \delta r = \left(x  \epsilon y, \epsilon x + y ,z\right) = r + \left( \epsilon y, \epsilon x ,0\right) [/latex], so that [latex] \delta x =  \epsilon y[/latex] and [latex] \delta y =  \epsilon x[/latex].




#3
Jul1409, 02:38 AM

P: 11

thanks, that's what I was looking for.



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