Calculating Orbits of Groups: SO(3)

[rdc30ynow]

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

 

[marlon]

What in heaven's name is the orbit of a group ?
Could you explain; please ?

marlon

 

[rdc30ynow]

group theory : orbits

if you let A be a group and G be an action on that group with a being a point in A. The set of all the images of the permutations of x by g in G on A is the orbit.

and here's the obligatory mathworld link: http://mathworld.wolfram.com/GroupOrbit.html

example : the orbit of the rotation group SO(2) is a circle.

( ... but I've been teaching myself all this, so there is a chance that I am completely wrong)