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Example of Non-Orthogonal Coordinates

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  Example of Non-Orthogonal Coordinates "F. Russell" <fr@random.info> - 2018-06-28 15:37 +0000
    Re: Example of Non-Orthogonal Coordinates Alan Folmsbee <omnilobe@gmail.com> - 2018-06-28 08:56 -0700
      Re: Example of Non-Orthogonal Coordinates Edward Prochak <edprochak@gmail.com> - 2018-06-28 10:30 -0700
        Re: Example of Non-Orthogonal Coordinates Sergio <invalid@invalid.com> - 2018-06-28 14:10 -0500
      Re: Example of Non-Orthogonal Coordinates Libor Striz <poutnik4REMOVEnntp@CAPITALSgmail.com> - 2018-06-28 19:56 +0200
    Re: Example of Non-Orthogonal Coordinates Puppet_Sock <puppet_sock@hotmail.com> - 2018-06-28 11:45 -0700

#692099 — Example of Non-Orthogonal Coordinates

Orthogonal coordinate systems are the most common
because they are easy to use.  Wikipedia has a list
of orthogonal coordinate systems:

https://en.wikipedia.org/wiki/Orthogonal_coordinates

I need some examples of non-orthogonal coordinate systems.
The reason is that ALL textbooks present non-orthogonal
systems in a totally general way and I want to practice on some
actual examples rather than dry generalized systems.

Can anyone provide an example or examples of non-orthogonal
coordinate systems?  By an example I mean the actual functions
that relate the Cartesian variables (x, y, z) to the
non-orthogonal coordinates (q1, q2, q3): x=f1(q1, q2, q3),
y=f2(q1, q2, q3), z=f3(q1, q2, q3) or the inverse relations.

I have searched and searched but can find no examples of
non-orthogonal coordinates.  Skew coordinates are non-orthogonal
but I am looking for more complicated examples.

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#692101

On Thursday, June 28, 2018 at 5:38:18 AM UTC-10, F. Russell wrote:
> Orthogonal coordinate systems are the most common
> because they are easy to use.  Wikipedia has a list
> of orthogonal coordinate systems:
> 
> https://en.wikipedia.org/wiki/Orthogonal_coordinates
> 
> I need some examples of non-orthogonal coordinate systems.
> The reason is that ALL textbooks present non-orthogonal
> systems in a totally general way and I want to practice on some
> actual examples rather than dry generalized systems.
> 
> Can anyone provide an example or examples of non-orthogonal
> coordinate systems?  By an example I mean the actual functions
> that relate the Cartesian variables (x, y, z) to the
> non-orthogonal coordinates (q1, q2, q3): x=f1(q1, q2, q3),
> y=f2(q1, q2, q3), z=f3(q1, q2, q3) or the inverse relations.
> 
> I have searched and searched but can find no examples of
> non-orthogonal coordinates.  Skew coordinates are non-orthogonal
> but I am looking for more complicated examples.

Spherical coordinates using 
radius
tilted equator angle value A
tilted equator angle value B

tilted equator angle C


four coordinates to define any point

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#692109

On Thursday, June 28, 2018 at 11:56:47 AM UTC-4, Alan Folmsbee wrote:
> On Thursday, June 28, 2018 at 5:38:18 AM UTC-10, F. Russell wrote:
> > Orthogonal coordinate systems are the most common
> > because they are easy to use.  Wikipedia has a list
> > of orthogonal coordinate systems:
> > 
> > https://en.wikipedia.org/wiki/Orthogonal_coordinates
> > 
> > I need some examples of non-orthogonal coordinate systems.
> > The reason is that ALL textbooks present non-orthogonal
> > systems in a totally general way and I want to practice on some
> > actual examples rather than dry generalized systems.
> > 
> > Can anyone provide an example or examples of non-orthogonal
> > coordinate systems?  By an example I mean the actual functions
> > that relate the Cartesian variables (x, y, z) to the
> > non-orthogonal coordinates (q1, q2, q3): x=f1(q1, q2, q3),
> > y=f2(q1, q2, q3), z=f3(q1, q2, q3) or the inverse relations.
> > 
> > I have searched and searched but can find no examples of
> > non-orthogonal coordinates.  Skew coordinates are non-orthogonal
> > but I am looking for more complicated examples.
> 
> Spherical coordinates using 
> radius
> tilted equator angle value A
> tilted equator angle value B
> 
> tilted equator angle C
> 
> 
> four coordinates to define any point

Alan,
Spherical polar coordinate only require 2 angles.
the third coordinate is the radius.

three coordinates to define any point.
Still orthogonal coordinate system.

Sorry Mr. Russel,
 I cannot contribute a non-orthogonal example.
Wonderful question. Please post if you  find other examples.

Also, perhaps someone in the moderated sci.physics.research
group can help.

ed

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#692121

On 6/28/2018 12:30 PM, Edward Prochak wrote:
> On Thursday, June 28, 2018 at 11:56:47 AM UTC-4, Alan Folmsbee wrote:
>> On Thursday, June 28, 2018 at 5:38:18 AM UTC-10, F. Russell wrote:
>>> Orthogonal coordinate systems are the most common
>>> because they are easy to use.  Wikipedia has a list
>>> of orthogonal coordinate systems:
>>>
>>> https://en.wikipedia.org/wiki/Orthogonal_coordinates
>>>
>>> I need some examples of non-orthogonal coordinate systems.
>>> The reason is that ALL textbooks present non-orthogonal
>>> systems in a totally general way and I want to practice on some
>>> actual examples rather than dry generalized systems.
>>>
>>> Can anyone provide an example or examples of non-orthogonal
>>> coordinate systems?  By an example I mean the actual functions
>>> that relate the Cartesian variables (x, y, z) to the
>>> non-orthogonal coordinates (q1, q2, q3): x=f1(q1, q2, q3),
>>> y=f2(q1, q2, q3), z=f3(q1, q2, q3) or the inverse relations.
>>>
>>> I have searched and searched but can find no examples of
>>> non-orthogonal coordinates.  Skew coordinates are non-orthogonal
>>> but I am looking for more complicated examples.
>>
>> Spherical coordinates using 
>> radius
>> tilted equator angle value A
>> tilted equator angle value B
>>
>> tilted equator angle C
>>
>>
>> four coordinates to define any point
> 
> Alan,
> Spherical polar coordinate only require 2 angles.
> the third coordinate is the radius.
> 
> three coordinates to define any point.
> Still orthogonal coordinate system.
> 
> Sorry Mr. Russel,
>  I cannot contribute a non-orthogonal example.
> Wonderful question. Please post if you  find other examples.
> 
> Also, perhaps someone in the moderated sci.physics.research
> group can help.
> 
> ed
> 

Cylindrical coordinates


and you can make up some, it is just mapping from one to the other

like 1/x, 1/y, and 1/z  system, inversion w respect to unit sphere

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#692111

Alan Folmsbee <omnilobe@gmail.com> Wrote in message:
>
> 
> Spherical coordinates using 
> radius
> tilted equator angle value A
> tilted equator angle value B
> 
> tilted equator angle C
> 
> 
> four coordinates to define any point
> 

3 ones. 

Radius, angle fi and angle theta.

Geographic coordinates ( latitude, longitude and altitude) are de
 facto spherical coordinates.
-- 
Libor Striz aka Poutnik ( a pilgrim/wanderer/wayfarer)

"Humour is the only effective weapon against stupidity."
Miloš Forman


----Android NewsGroup Reader----
http://usenet.sinaapp.com/

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#692117

On Thursday, June 28, 2018 at 11:38:18 AM UTC-4, F. Russell wrote:
[snip]
> I have searched and searched but can find no examples of
> non-orthogonal coordinates.  Skew coordinates are non-orthogonal
> but I am looking for more complicated examples.

Sure. 

Basis coordinates of crystal structures where the
unit cell is a six-sided box where the sides don't meet
in 90 degree angles. I spent all of 2 minutes looking
for an example of such but didn't find.

In a similar line, coordinates for lattice structures
based on hexagonal prisms. The first two coords are
60 degrees apart, and the third is perpendicular to
the first two, pointing along the axis of the prism.

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