- #1
daxowax
- 4
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Hello,
I have a maybe unusual question. In a paper, I recently found the equation $$\mathcal{L}_v(v_i dx^i) = (v^j \partial_j v_i + v_j \partial_i v^j) dx^i$$
Where [itex]v[/itex] denotes velocity, [itex]x[/itex] spatial coordinates and [itex]\mathcal{L}_v[/itex] the Lie derivative with respect to [itex]v[/itex]. Now I'm an undergraduate who understands very little of differential geometry. Besides this, my paper does not require any knowledge of this discipline.
Is there someone who could help me out with some rough explanation or short derivation of this formula?
I have a maybe unusual question. In a paper, I recently found the equation $$\mathcal{L}_v(v_i dx^i) = (v^j \partial_j v_i + v_j \partial_i v^j) dx^i$$
Where [itex]v[/itex] denotes velocity, [itex]x[/itex] spatial coordinates and [itex]\mathcal{L}_v[/itex] the Lie derivative with respect to [itex]v[/itex]. Now I'm an undergraduate who understands very little of differential geometry. Besides this, my paper does not require any knowledge of this discipline.
Is there someone who could help me out with some rough explanation or short derivation of this formula?