Register to reply

Rotational symmetry

by adkinje
Tags: rotational, symmetry
Share this thread:
adkinje
#1
Jun6-09, 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?
Phys.Org News Partner Physics news on Phys.org
Step lightly: All-optical transistor triggered by single photon promises advances in quantum applications
The unifying framework of symmetry reveals properties of a broad range of physical systems
What time is it in the universe?
EricAngle
#2
Jul9-09, 11:46 PM
P: 4
I haven't watched the video, but if you perform a rotation 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].
adkinje
#3
Jul14-09, 02:38 AM
P: 11
thanks, that's what I was looking for.


Register to reply

Related Discussions
What is the difference between dynamical symmetry and geometrical symmetry? Classical Physics 5
How does a system consisting of two nuclei have rotational symmetry? General Physics 5
Finding a Rotational Symmetry Group Calculus & Beyond Homework 5
Rotational spectra - thermal population of rotational levels Advanced Physics Homework 0
Gauge symmetry and symmetry breaking High Energy, Nuclear, Particle Physics 2