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Homework Help: Please explain about general coordiante

  1. Mar 20, 2010 #1
    Hello.

    In Arfken(6rd edi.), p.104 around eqn(2.3),

    ~~In general, these unit vectors will depend on the position in space. Then a vector may be written,
    [tex]V=\hat {q_{1}}V_{1}+ \hat q_{2} V_{2}+ \hat q_{3} V_{3}[/tex]
    [tex] \underline{\mbox{but the coordinate or position vector is different in general,}}\\
    r \neq \hat q_{1} V_{1}+ \hat q_{2} V_{2}+ \hat q_{3} V_{3} , [/tex]
    [tex]
    \mbox{as the special case}[/tex]
    [tex] r=r\hat r \\\\\\\ \mbox{for spherical polar coordinates and}\\\\\\\\ r= \rho \hat \rho +z \hat z \\\\\\\\\\ \mbox {for cylindrical coordinates demonstrate. \cdots} [/tex]
    What's the meaning of the underlined sentence?
     
  2. jcsd
  3. Mar 21, 2010 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hello merrypark3! :smile:

    It means that the vectors from the point V have nothing to do with the vector of the point V.

    For example, in spherical coordinates, the vector of V is simply r in the er direction (θ and φ don't matter, and indeed eθ and eφ aren't even defined at the origin), and in cylindrrical coordinates, the vector of V is simply ρ in the eρ direction and z in the ez direction (φ doesn't matter). :wink:
     
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