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MathGroup Archive 2004

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derivatives in cylindrical coords??

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51260] derivatives in cylindrical coords??
  • From: "news" <anonym at bamboo.com>
  • Date: Sun, 10 Oct 2004 05:52:34 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

are derivative rules different for cylindrical coordinates??  for example, 
taking derivative of unit vectors in Cartesian coords with base units vector 
{x, y, z}  gives:
d/dx {x, 0, 0} = {1, 0, 0}
d/dy {0, y, 0} = {0, 1, 0}
d/dz {0, 0, z} = {0, 0, 1}
now, for cylindrical coords where base vectors are: {r, phi, z}, does this 
hold??
d/dr {r, 0, 0} = {1, 0, 0}
d/dphi {0, phi, 0} = {0, 1, 0}
d/dz {0, 0, z} = {0, 0, 1}
I'm finding that it doesn't work , becuase if you cross d/dr with d/dphi in 
cylindrical coords, you get {0,0,0}, and you should get {0,0,1}, so 
something is missing in this derivative process, no???  Can anyone help?? 


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