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norm of a cylindrical vector?

Posted 11 years ago

The angle of a cylindrical vector should not contribute to its length, so I was expecting the root of 25, or 5. Where did I go wrong? Mathematica 9 newbie

SetCoordinates[Cylindrical[r, \[Theta], z]]
CoordinateSystem
w = {3, 2, 4}
Norm[w]
(w . w)^.5
CoordinateSystem

I get;

Cylindrical[r, \[Theta], z]
Cylindrical
{3, 2, 4}
Sqrt[29]
5.38516
Cylindrical
POSTED BY: T Zintel
8 Replies

The code you have requires loading the old package. The built-in vector analysis functions have different names or different ways to obtain the same output. See http://reference.wolfram.com/language/Compatibility/tutorial/VectorAnalysis.html or its built-in equivalent, Compatibility/tutorial/VectorAnalysis under Help - Wolfram Documentation.

The above tutorial suggests replacing DotProduct from the old package with a user function that converts the vectors to Cartesian, then takes the ordinary Dot product.

In[1]:= dotProduct[a_, b_, chart_] := 
 CoordinateTransform[chart -> "Cartesian", a].CoordinateTransform[ chart -> "Cartesian", b]

In[2]:= dotProduct[{3, 2, 4}, {3, 2, 4}, "Cylindrical"] // N

Out[2]= 25.

Using the package works for me with 10.0.0 and 10.0.1.

In[1]:= Needs["VectorAnalysis`"]

General::obspkg: VectorAnalysis` is now obsolete. The legacy version being loaded may conflict with
     current functionality. See the Compatibility Guide for updating information.

In[2]:= DotProduct[{3, 2, 4}, {3, 2, 4}, Cylindrical]

                     2           2
Out[2]= 16 + 9 Cos[2]  + 9 Sin[2]

In[3]:= Simplify[%]

Out[3]= 25

In[4]:= $Version

Out[4]= 10.0 for Microsoft Windows (64-bit) (June 29, 2014)

The attached notebook has three examples - your code without loading the package, your code after loading the package, and the new method.

Attachments:
POSTED BY: Bruce Miller
Posted 11 years ago

This question fell from strange cylindrical results as well. The problem I'm working is naturally cylindrical. I set Coords to Cyl and got to work. When I noticed things were not coming out as expected I started back tracking and found my Dots were not working correctly.

The w of 3,2,4 was fabricated as a test of Dot because it would give obvious results in Cyl & Cart coordinates. I did see good documentation on translating between coordinate systems, but that really doesn't suit my needs for this case.

Can I get someone to confirm if the above snippet does / doesn't work for them in mathematica 10?

POSTED BY: T Zintel

I've sometimes gotten strange results with spherical or cylindrical coordinates. These can be avoided by transforming to good old Cartesian coordinates. With x=r cos\theta, y=r sin\theta, z=z , wcyl={3,2,4} becomes wcart={3 cos(2), 3 sin(2), 4} , etc. Do you really have theta=2 radians? Actually, it looks like w={3,2,4} is already in Cartesian coordinates, so w.w=29.

POSTED BY: S M Blinder

Unless I'm missing something obvious....I'm stumped

Posted 11 years ago

Thanks for the quick replies. I did a unistall / reinstall / upgrade before my last message hoping it would help as well. Today I tried a fresh installation of 10.0.1.0 on a linux machine expecting that too clear things up. Surprisingly it didn't.

I open a new notebook, execute:

SetCoordinates[Cylindrical[r, \[Theta], z]]
CoordinateSystem
w = {3, 2, 4}
Norm[w]
(w.w)^.5
CoordinateSystem
DotProduct[{3, 2, 4}, {3, 2, 4}, Cylindrical]

and get:

SetCoordinates[Cylindrical[r, \[Theta], z]]
CoordinateSystem
{3, 2, 4}
Sqrt[29]
5.38516
CoordinateSystem
DotProduct[{3, 2, 4}, {3, 2, 4}, Cylindrical]

All the Coordinate system command appear to go unrecognized?

Any thoughts?

POSTED BY: T Zintel
Posted 11 years ago

I'm still getting the same thing. As you can see Mathematica does not appear to be recognizing any vector calculus statements. I upgraded to 10.1 but it didn't help.

DotProduct[{3, 2, 4}, {3, 2, 4}, Cylindrical] 

Just echoed like other non recognized commands.

If I execute

`Needs["VectorAnalysis`"]`

I get closer, but still wrong and kinda going in the wrong direction.

What am I missing?

POSTED BY: T Zintel

The upgrade was unnecessary (at least for this question) as I am using version 7. With version 10 , you dont need to use the Needs ["VectorAnalysis"] as this functionality is already included

DotProduct[{3,2,4},{3,2,4},Cylindrical]//N

this should give you the answer you need / expect .

Not sure why you are getting this problem, but I would consider re-installing Mathematica

http://reference.wolfram.com/language/VectorAnalysis/ref/DotProduct.html

DotProduct seems to give the answer you are expecting

DotProduct[{3,2,4},{3,2,4},Cylindrical]//N

25

Since you have already set the coordinate system., including the "Cylindrical" option is optional

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