Yes. It would be a good idea to restrict yourself to diagonal metric
tensors (orthogonal coordinate system) then inverting the metric tensor
is simple and the Jacobian matrix is also diagonal. If you have a
metric tensor you would use the Christoffel symbols to calculate the
derivatives of the basis vectors. For a spherical coordinate system
(r,theta,phi) the diagonal of metric tensor would be
(1,r**2,r**2*sin(theta)**2).
On 11/21/2014 11:53 AM, Lukas Zorich wrote:
El jueves, 20 de noviembre de 2014 10:45:50 UTC-3, brombo escribió:
You might wish to be more general and implement vector
analysis as a function of a metric tensor. See the following
link -
http://en.wikipedia.org/wiki/Curvilinear_coordinates#Vector_operations
<http://en.wikipedia.org/wiki/Curvilinear_coordinates#Vector_operations>
Can you explain me a bit more? you mean that instead of calculating
dot product or cross product in a specific coordinate system, I
calculate that using the metric tensor as it appeared in the wikipedia
article?
El jueves, 20 de noviembre de 2014 10:45:50 UTC-3, brombo escribió:
You might wish to be more general and implement vector analysis as
a function of a metric tensor. See the following link -
http://en.wikipedia.org/wiki/Curvilinear_coordinates#Vector_operations
<http://en.wikipedia.org/wiki/Curvilinear_coordinates#Vector_operations>
On 11/19/2014 10:34 PM, Lukas Zorich wrote:
Thanks Jason!
El miércoles, 19 de noviembre de 2014 19:17:24 UTC-3, Jason Moore
escribió:
Lukas,
Sachin Joglekar developed the vector package this past
summer. I was his GSoC mentor on the project. You can check
out this implemented of the Cartesian coordinate system:
https://github.com/sympy/sympy/blob/master/sympy/vector/coordsysrect.py
<https://github.com/sympy/sympy/blob/master/sympy/vector/coordsysrect.py>
You'd basically need to create a class for spherical that has
this same functionality. You may be able to create a
spherical class that converts the input to Cartesian and just
manages a Cartesian system behind the scenes. Or method can
be implemented explicitly using spherical coordinates.
Jason
moorepants.info <http://moorepants.info>
+01 530-601-9791
On Wed, Nov 19, 2014 at 5:05 PM, Lukas Zorich
<lukas....@gmail.com> wrote:
Hi everyone,
I am Lukas from Chile, pursuing a degree in Computer
Science and with interests in mathematics. I would like
to start contributing to sympy. Reading through the
mailing list, I saw this
<https://groups.google.com/forum/?hl=es-419#%21topic/sympy/4SIr_6iW6v4>post
that says that the Spherical Coordinates System isn't
implemented yet, so I would like to start from there. I
wanted to know who can I ask to give me further
information about this specific functionality, or things
I need to know before implementing this (not about the
theory, but about the concrete implementation of the
spherical system in the vector module).
Thanks :)!
Lukas
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