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Re: Example of Non-Orthogonal Coordinates

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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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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

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