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MathGroup Archive 2007

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Re: CrossProduct in Spherical Coordinates

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75342] Re: CrossProduct in Spherical Coordinates
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 25 Apr 2007 05:45:43 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • 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]

Here you tell Mathematica that _the given vectors are expressed_ in 
spherical coordinates. You are not asking Mathematica to convert from 
one system of coordinates (which one?) to spherical coordinates.

> Out[2]=
> {0,0,0}
> 
> Why? Isn't the result supposed to be {0,0,1}, even in spherical
> coordinates?

No. The point (0, 0, 1) in Cartesian coordinates is (1, 0, 0) in 
spherical coordinates.

The following examples should illustrate how to use the package.

In[1]:=
<< "Calculus`VectorAnalysis`"

In[2]:=
CoordinateSystem[]

Out[2]=
Cartesian[]

In[3]:=
pt1 = CoordinatesFromCartesian[{1, 0, 0}, Spherical]

Out[3]=
     Pi
{1, --, 0}
     2

In[4]:=
pt2 = CoordinatesFromCartesian[{0, 1, 0}, Spherical]

Out[4]=
     Pi  Pi
{1, --, --}
     2   2

In[5]:=
pt3 = CrossProduct[pt1, pt2, Spherical]

Out[5]=
{1, 0, 0}

In[6]:=
CoordinatesToCartesian[pt3, Spherical]

Out[6]=
{0, 0, 1}

In[7]:=
SetCoordinates[Spherical[r, theta, phi]]

Out[7]=
Spherical[r, theta, phi]

In[8]:=
CoordinateRanges[]

Out[8]=
{0 <= r < Infinity, 0 <= theta <= Pi, -Pi < phi <= Pi}

In[9]:=
pt1 = CoordinatesFromCartesian[{1, 0, 0}]

Out[9]=
     Pi
{1, --, 0}
     2

In[10]:=
pt2 = CoordinatesFromCartesian[{0, 1, 0}]

Out[10]=
     Pi  Pi
{1, --, --}
     2   2

In[11]:=
pt3 = CrossProduct[pt1, pt2]

Out[11]=
{1, 0, 0}

In[12]:=
CoordinatesToCartesian[pt3]

Out[12]=
{0, 0, 1}

Regards,
Jean-Marc



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