Inverse Function of Curl

Discussion in 'Physics' started by Michael Lin, Nov 6, 2005.

  1. Michael Lin

    Thread Starter Member

    Sep 20, 2005
    13
    0
    Mathematically, I know that to recover a vector from the gradient of a vector, I need to integrate and the solution is not unique.
    If i want to recover the vector from the curl of a vector, is there a standard way to do it? How? I'm pretty sure this vector is not unique too, correct?

    Thanks.
    Michael
     
  2. cookevillain

    New Member

    Dec 1, 2005
    4
    0
    Michael,

    One thing to keep in mind is that there is no such thing as the curl of a vector: you can only find the curl of a vector field. This out of the way, you are right: there is no unique way to get the original vector field back: the curl is a differential operator so shifting everything by a constant vector would preserve it. Moreover, there are plenty of fields with zero curl. Another complication arises from the question: what is the domain of the field? If your field is defined on the whole R^3 (euclidean space), techniques based on Stokes' theorem can help, otherwise one has to get a bit more sophisticated. Hope this helps.

    C-villain

     
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