Re: vectors in polar coordinates
- To: mathgroup@smc.vnet.net
- Subject: [mg11791] Re: vectors in polar coordinates
- From: Paul Abbott <paul@physics.uwa.edu.au>
- Date: Sat, 28 Mar 1998 00:25:26 -0500
- Organization: University of Western Australia
- References: <6fd6aa$6ck@smc.vnet.net>
Michael Milirud wrote:
> If I want to add 2 vectors of which I have a polar (cylindrical)
> representation I am forced to do something like
>
> << Calculus`VectorAnalysis`
> SetCoordinates[Cylindrical]
> a={100, -115*Pi/180, 0}
> b={200, -30*Pi/180, 0}
> A=CoordinatesToCartesian[a, Cylindrical] B=CoordinatesToCartesian[b,
> Cylindrical] d=A+B
> D=CoordinatesFromCartesian[d, Cylindrical]
>
> and that is a HECK longer to do then by hand.
Actually, isn't that exactly how you WOULD do it by hand?
>There's got to be something simplier like:
> {100, -115*Pi/180, 0} + {200, -30*Pi/180, 0}
After loading the package
In[1]:= << "Calculus`VectorAnalysis`"
and setting the coordinate system
In[2]:= SetCoordinates[Cylindrical];
you could use CirclePlus (a built-in infix operator) as follows:
In[3]:= (a_) \[CirclePlus] (b_) :=
CoordinatesFromCartesian[CoordinatesToCartesian[a] +
CoordinatesToCartesian[b]]
This expression will format nicely in a Notebook (especially if you are
using TraditionalForm for input and output). Now you can use this to
add two vectors in whatever default coordinate system you are using,
e.g.,
In[4]:= a = {100, -((115*Pi)/180), 0};
In[5]:= b = {200, -((30*Pi)/180), 0};
In[6]:= N[a \[CirclePlus] b]
Out[6]= {231.271,-0.96892,0}
> Also how do I find a magnitude of a vector. The Abs[] doesn't support
> this. Sqrt[d[[1]]^2+d[[2]]^2+d[[3]]^2]
How about Sqrt[d.d]. Alternatively, you could try overloading Abs[]. A
better solutions is to use a DoubleBracketingBar:
In[7]:= \[LeftDoubleBracketingBar] d_ \[RightDoubleBracketingBar]:=
Sqrt[d . d]
In[8]:= \[LeftDoubleBracketingBar] {1, 1, 1}
\[RightDoubleBracketingBar]
Out[8]= Sqrt[3]
Again, this input will format nicely in a Notebook.
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul@physics.uwa.edu.au AUSTRALIA
http://www.pd.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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