Implementation of multiple types of coordinate systems for vectors

[Karan Sharma]

Greetings SymPy community :)

I am a student. I love mathematics. I am new to open source. I want to start working on "Implementation of multiple types of coordinate systems for vectors". Couple of things i wanted to ask:

• What is the status of this project, has someone worked on it already?
• Where can i start ?
• Since i am only a beginner can some one sort of mentor me, i swear i wont disturb much :)

Thanks

[Robert Lee]

I'm also interested in assisting in this development as well... I use sympy in several projects so I think its about time I give back a little.

I can help out some in terms of getting the project started; however, I'm not as familiar with the full core of sympy so another set of eyes on the project would be nice.

rbl

[Aaron Meurer]

A lot of discussion happened on this idea on this list last spring.
Although none of the projects ended up being accepted, the discussions
that happened are still relevant.

Aaron Meurer

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[Alan Bromborsky]

Suggest you start with the metric tensor, g_{ij}, and then calculate the Christoffle symbols, \Gamma_{ijk}, to calculate the partial derivatives of the basis vectors with respect to the coordinates.  See footnote on page 17 of attached document.  See section 2.3.2 of same document on how to calculate the normalized basis vectors and their partial derivatives.  For the coordinate systems you would be interested in the metric tensor is diagonal (orthogonal systems) but the basis vectors are not normalized.

For a spherical coordinate system the diagonal of the metric tensor (all other entries are zero) are -

 g=[1, r ** 2, r ** 2 * sin(th) ** 2]

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