| Highlights: |
- Example of Derivations.
- Vector Fields
- Integral curves of vector fields as One parameter groups
- Lie Groups
- Abelian (Commutative) and Non-Abelian (non-commutative)
- Is SO(2) an Abelian Lie Group?
SO(2) is an Abelian Lie Group. The elements of SO(2)
correspond to the action of rotation in \Re^2 about the
origin, and two subsequent rotations \theta and \phi yield
a net rotation of \theta + \phi which equivalent to rotation
by \phi first and then \theta. Algebriacally it can be easily
shown that SO(2) is indeed Abelian by multiplying the
matrices representing two different elements of SO(2).
- Left Action and Right Action
- Left Action is usually used when we have perform some operation in the World (Static) reference frame. Right Action is usually used when we have to do transformations in Body coordinate frame.
- Examples of Lie Groups
- Lie Brackets
- Is a Lie bracket of two everywhere orthogonal vector fields necessarily zero everywhere?
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