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Use symbolic vectors for physics?

GROUPS:

Dear all

It is possible to use Symbolic Vector to perform the typical vector operations we use in Physics (for example, electromagnetism)? I mean, for example, applying vector identities to vector fields, like

rot ( rot (A)) = grad( div(A)) - laplacian(A)

o, more interesting for me, to obtain dispersion relations from differential equations. I have seen the documentation for symbolic vectors and tensors, but I assume that there should be more detailed information somewhere. There is already a thread on a closely related subject

http://community.wolfram.com/groups/-/m/t/1127218

but I am not able to obtain a practical conclusion.

Is there an example or tutorial of these type of calculations with Mathematica?

Thank you. Best wishes.

Carlos Soria-Hoyo Sevilla SPAIN

POSTED BY: Carlos Soria-Hoyo
Answer
21 days ago

The following Mathematica application may be of interest to you.

Grassmann Calculus, Geometric Algebra, Differential Forms

POSTED BY: David J M Park Jr
Answer
21 days ago

Carlos,

I have used the built-in vector operations found in the documentation:

Vector Tutorial

Vector Guide

Operations on Vectors

Is this what you want? These operations all work on symbolic vectors and should do what you want unless I am not understanding your request.

Regards,

Neil

POSTED BY: Neil Singer
Answer
20 days ago

Thank you for your answer, Neil.

You are right, of course. I manage with those vectors operations you refer to, by setting a coordinate system. But I am asking for these type of calculations:

example

that are very usual in physics books (usually to obtain dispersion relations).

Best wishes Carlos

POSTED BY: Carlos Soria-Hoyo
Answer
20 days ago

Carlos,

That should be Ok. The only issue that I have ever encountered is that you need to use variables in the matrix so WMA knows the dimensionality of your problem. For example, I would be careful using a single variable for a matrix because some operations assume the variables as scalars (or more accurately, they can handle either scalar or matrix arguments so a single variable is assumed to be scalar). So set k={{a,b},{c,d}} or k=Array[a,{2,2}]

Your equations can then be expressed using MatrixExp[], Div, Cross, Grad, etc

Documentation is here: Vector Analysis

POSTED BY: Neil Singer
Answer
20 days ago

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