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Please explain about general coordiante

  • Thread starter merrypark3
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  • #1
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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?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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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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