Re: CrossProduct in Spherical Coordinates

• To: mathgroup at smc.vnet.net
• Subject: [mg75336] Re: CrossProduct in Spherical Coordinates
• From: roland franzius <roland.franzius at uos.de>
• Date: Wed, 25 Apr 2007 05:42:32 -0400 (EDT)
• Organization: Universitaet Hannover
• References: <f0kbsf\$r1k\$1@smc.vnet.net>

```gogoant06 at yahoo.com.hk wrote:
> Dear all,
>
> I am really new to mathematica and I have met a damn simple problem.
>
> In[1]:=
> <<Calculus`VectorAnalysis`
>
> In[2]:=
> CrossProduct[{1,0,0},{0,1,0},Spherical]
>
> Out[2]=
> {0,0,0}
>
> Why? Isn't the result supposed to be {0,0,1}, even in spherical
> coordinates?

Take the cross product of the north polar vector with any pointing
towards the equator

In:
Assuming[r > 0 && R > 0,
FullSimplify[CrossProduct[{r, 0, phi}, {R, Pi/2, phi1}, Spherical]]]

Out:
{r*R, Pi/2, ArcTan[-Sin[phi1], Cos[phi1]]}

As you see, the lists in the arguments are the coordinates {r,theta,
phi} of the endpoints of the vectors, not their algebraic components in
what base so ever (could be cartesian or tangent space base).

--

Roland Franzius

```

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