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