Re: Vectors and Mathematica
- To: mathgroup@smc.vnet.net
- Subject: [mg11784] Re: Vectors and Mathematica
- From: tburton@brahea.com (Tom Burton)
- Date: Sat, 28 Mar 1998 00:25:20 -0500
- Organization: Brahea, Inc.
- References: <6fd5vi$6bu@smc.vnet.net>
On 26 Mar 1998 04:09:06 -0500, in comp.soft-sys.math.mathematica you
wrote:
>I'm really lost here. It seems there is almost NO support of simple
>vectors in Mathematica v.3.0
>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±00, -115*Pi/180, 0}
>b²00, -30*Pi/180, 0}
>AÈordinatesToCartesian[a, Cylindrical] BÈordinatesToCartesian[b,
>Cylindrical] d«B
>DÈordinatesFromCartesian[d, Cylindrical]
>
>and that is a HECK longer to do then by hand. There's got to be
>something simplier like:
>{100, -115*Pi/180, 0} + {200, -30*Pi/180, 0}
>
>or something...
>
>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]
>
>is simply hedious!!!
>
>Please help cause I'm really lost ;(
>
>Michael
>
>P.S. If possible, please also send a direct email to
>mmichael@idirect.com
>
Taking the second issue first, the length of a vector v is equal to
Sqrt[DotProduct[v,v]]. DotProduct is a function built into the package
Calculus`VectorAnalysis`, so you're home free there.
There seems to be no similar support for the sum of two vectors. Once
you understand a little about how packages work, it's easy to extend
that package to support this new function. Below is a small v. 3
notebook showing how to add a new function VectorSum, a trival
modification of DotProduct.
There are many holes is the functionality provided by the core and
standard packages. The transparency of Mathematica partially makes up
for a lot of these deficiencies.
Tom Burton Brahea, Inc. tburton@brahea.com
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Notebook[{
Cell["Load the package we want to extend:", "Text"],
Cell[BoxData[
\(<< Calculus`VectorAnalysis`\)], "Input"],
Cell["\<\
What we want is a function similar to DotProduct, but that forms a sum:\
\>", "Text"],
Cell[CellGroupData[{
Cell[BoxData[
\(\(?DotProduct\)\)], "Input"],
Cell[BoxData[
\("DotProduct[v1, v2] gives the dot product (sometimes called inner
\
product or scalar product) of the two vectors v1, v2 in three space in
the \
default coordinate system. DotProduct[v1, v2, coordsys] gives the dot \
product of v1 and v2 in the coordinate system coordsys."\)], "Print"]
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Cell[CellGroupData[{
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Let's call our new function VectorSum. We'll pattern the usage after \
DotProduct:\
\>", "Text"],
Cell[BoxData[
\(\(VectorSum::"\<usage\>" "\<VectorSum[v1, v2] gives the sum of the two vectors v1, v2 in
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space in the default coordinate system. VectorSum[v1, v2, coordsys]
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the sum of v1 and v2 in the coordinate system coordsys.\>"; \)\)],
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We'll pattern the actual function after DotProduct, too. To see it, we
need \
to clear the read-lock:\
\>", "Text"],
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Cell["\<\
Now let's enter the Private subcontext, where we will want to add the
new \
function:\
\>", "Text"],
Cell[CellGroupData[{
Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
\(?? DotProduct\)], "Input"],
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\("DotProduct[v1, v2] gives the dot product (sometimes called inner
\
product or scalar product) of the two vectors v1, v2 in three space in
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coordsys_: $CoordinateSystem]\ :
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cv1\ . \ cv2\ /; \
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There is a small trick, which took me a little while to figure out. We
need \
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Cell["\<\
Other than that, making VectorSum from DotProduct is easy: change cv1 .
cv2 \
to $CTFromCart[cv1+cv2,cs]. I guessed the existence of CTFromCart from
the \
presence of CTToCart. \
\>", "Text"],
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(Looking at this is how I knew to clear $CoordinateSystem.) Now return
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\>", "Text"],
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Cell[BoxData[
\(\(?VectorSum\)\)], "Input"],
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\("VectorSum[v1, v2] gives the sum of the two vectors v1, v2 in
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the sum of v1 and v2 in the coordinate system coordsys."\)], "Print"] },
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Seems like it's working. Now return to the Cylindrical coordinates and
try a \
few simple numerical examples:\
\>", "Text"],
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If you like the way this is working, it's easy to add the definitions
above \
to appropriate places in
Addons:StandardPackages:Calculus:VectorAnalysis.m.\ \>", "Text"],
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the \
package. The kernel told me everything I needed to know. This
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"."
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Tom Burton Brahea, Inc. 619/436-7436