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Divergence Simplification/Identities

  1. Oct 2, 2011 #1
    Quick question…

    what does the following simplify to? Can it be written in any other way?

    [itex]\nabla\bullet (a \bullet b)b [/itex]

    where a and b are vectors.

    Thanks,
     
  2. jcsd
  3. Oct 2, 2011 #2
    in general

    [tex]\nabla (\varphi \mathbf{F})=(\nabla \varphi)\bullet\mathbf{F}+\varphi (\nabla \bullet \mathbf{F})[/tex]

    let [tex]\varphi = \mathbf{a}\bullet \mathbf{b}[/tex]

    and [tex]\mathbf{F}=\mathbf{b}[/tex]
     
  4. Oct 2, 2011 #3
    Thanks, but I didn't think that [itex]\nabla\bullet (\mathbf{a} \bullet \mathbf{b})\mathbf{b} [/itex] was the same as [tex]\nabla (\varphi \mathbf{F})[/tex]... there's still a [tex]\bullet[/tex] between the [tex]\nabla [/tex] and the rest of the statement.

    Can you clarify?
     
  5. Oct 2, 2011 #4
    little mishtake...above should be

    [tex]\nabla \bullet (\varphi \mathbf{F})=(\nabla \varphi)\bullet\mathbf{F}+\varphi (\nabla \bullet \mathbf{F})[/tex]

    :tongue:
     
  6. Oct 3, 2011 #5
    Thanks, issacnewton.

    When substituting in [tex]\mathbf{a}\bullet \mathbf{b}[/tex] and [tex]\mathbf{b}[/tex] into the equation, it looks like it'd simplifies further.. but it looks like it'd be ugly. :yuck:

    Any good way of simplifying it?

    Thanks,
     
  7. Oct 3, 2011 #6
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