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cross-product in cylindrical problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg51258] cross-product in cylindrical problem
*From*: "news" <anonym at bamboo.com>
*Date*: Sun, 10 Oct 2004 05:52:32 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
I'm really puzzled by this behavior of Mathematica, I have two vectors in
cylindrical coordinates and would like to take their cross-product in
cylindrical, but it seems to give me incorrect answer, see below:
define parametric path {r,phi,z}
In[110]:=
f[\[Rho]_, \[Phi]_] = {\[Rho], \[Phi], 0}
Out[110]=
{\[Rho], \[Phi], 0}
take derivates of path w.r.t. r then w.r.t phi, get {1,0,0}, and {0,1,0}
In[113]:=
v1 = D[f[\[Rho], \[Phi]], \[Rho]]
v2 = D[f[\[Rho], \[Phi]], \[Phi]]
Out[113]=
{1, 0, 0}
Out[114]=
{0, 1, 0}
then cross them in cylindrical coords, and should get {0,0,1}, but instead
get wrong answer below
In[117]:=
n = CrossProduct[v1, v2, Cylindrical[\[Rho], \[Phi], z]] // FullSimplify
Out[117]=
{0, 0, 0}
As you can see, when I cross {1,0,0} with {0,1,0} in cylindrical coords, I
get {0,0,0}, when I should be getting {0,0,1}.
Can anyone help?
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