So(3) — 55 discussions

  1. M

    Graduate Rotational group SO(3) in classical mechanics

    Hi! This is my first post here. I'm currently studying analytical/classical mechanics and have some problems understanding how the Lie algebra is formed in relation to the SO(3) group of rotations. My problem is this: Given a matrix representation R of some rotation around a fixed axis, we...
    • m_dronti
    • Thread
    • Classical Classical mechanics Group Mechanics Rotational So(3)
    • Replies: 2
    • Forum: Mechanics
  2. J

    Graduate What are the v_j vectors in Cahn's representation of the Lie algebra of SO(3)?

    Hi all, I asked this on the Quantum Physics board but didn't get a response. I'm reading Cahn's book on semi-simple lie algebras and their representations. http://www-physics.lbl.gov/~rncahn/book.html In chapter 1, he attempts to build a (2j+1)-dimensional representation T of the Lie...
  3. belliott4488

    Graduate Why is SU(2) a double cover of SO(3) and what does that mean?

    What's the correct way to state the relationship between these two Lie groups? One is the "covering group" of the other, right? Okay, then - what's that mean, to a non-expert? I know the basics, i.e. SO(3) can be represented by rotation matrices in 3-space, and U(2) does the same in a...
  4. J

    Can you express rotations as products of reflections in SO(3)?

    1) Let P,Q be planes through the origin in R3. Let Rp, Rq be the corresponding reflections. Is Rp*Rq (where * denotes "composition") in SO(3) or O(3)/SO(3)? What is the axis of rotation of Rp*Rq? 2) For a fixed A in SO(3) show that there are infinitely many pairs of planes P,Q such that...
  5. R

    Calculating Orbits of Groups: SO(3)

    group theory : orbits hi. I'm trying to calculate the orbits of some simple groups. I have found many explanations of what they are, but no example calculations. does anyone have any ideas where to look. I'm trying to calculate the orbit of SO(3). thanks