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Integral of force squared

  1. Jun 13, 2009 #1
    The path integral of force is the work, something that has a clear physical meaning we can relate to. My question is, what is the physical interpretation for the L2 norm of the force along a path? (integral of the force squared, basically):

    [tex]\left(\int_\Gamma F \cdot F \right)^{\frac{1}{2}}[/tex]

    If a particle takes the path from point A to B which minimizes the work, then the least amount of external energy was expended moving it from point A to B. Can we analogously characterize the type of paths between 2 points that minimize the L2 norm of the force.

    Thanks!
     
    Last edited: Jun 13, 2009
  2. jcsd
  3. Jun 13, 2009 #2

    gabbagabbahey

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    Do you mean:

    [tex]\left(\int_\Gamma (\mathbf{F} \cdot \mathbf{F})ds \right)^{\frac{1}{2}}[/tex]

    ?
     
  4. Jun 13, 2009 #3
    Yes, of course. F:R3->R3, [itex]\Gamma:[0,1]->\textbf{R}^3[/itex]
     
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