Message Boards Message Boards

0
|
7686 Views
|
4 Replies
|
1 Total Likes
View groups...
Share
Share this post:

Use symbolic vectors for physics?

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

4 Replies

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

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

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

The following Mathematica application may be of interest to you.

Grassmann Calculus, Geometric Algebra, Differential Forms

Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract