Differentiating vector function [Mathematica]

Click For Summary
SUMMARY

The discussion focuses on differentiating a vector function in Mathematica, specifically the function \(\hat{u}=\left\langle\bar{u}+\bar{r}\frac{(1+\gamma)}{r(r+\bar{u}\cdot \bar{r})}\right\rangle\). The user seeks to demonstrate the equality \(\frac{\partial\hat{u}}{\partial\gamma}=(\bar{r}-\bar{u}(\bar{u}\cdot\bar{r})\frac{1}{r(r+\bar{u}\cdot\bar{r})}\) using Mathematica, confirming its correctness based on a referenced paper. The inquiry highlights the absence of gamma dependence in the derivation process, prompting a request for clarification on how to achieve this in Mathematica.

PREREQUISITES
  • Familiarity with vector calculus and differentiation
  • Understanding of Mathematica syntax and functions
  • Knowledge of normalization techniques in vector functions
  • Basic comprehension of the parameters involved, such as \(\gamma\), \(\bar{u}\), and \(\bar{r}\)
NEXT STEPS
  • Explore Mathematica's differentiation functions, specifically D[] for symbolic differentiation
  • Research vector normalization techniques in Mathematica
  • Study the implications of parameter dependencies in vector functions
  • Review literature on vector calculus to understand component-wise differentiation
USEFUL FOR

Mathematicians, physicists, and engineers working with vector calculus in Mathematica, particularly those needing to differentiate complex vector functions.

Phudge
Messages
1
Reaction score
0
Hi.
So I have this vector function which I need to differentiate, it is however very tricky to do by hand, so I'm doing it in Mathematica.
[tex]\hat{u}=\left\langle\bar{u}+\bar{r}\frac{(1+\gamma)}{r(r+\bar{u}\cdot \bar{r})}\right\rangle[/tex]
(The brackets denote normalisation)

I want to do this differentiation for the different components of r but first I want to show:

[tex]\frac{\partial\hat{u}}{\partial\gamma}=(\bar{r}-\bar{u}(\bar{u}\cdot\bar{r})\frac{1}{r(r+\bar{u}\cdot\bar{r})}[/tex]
which I know to be correct from the paper I am basing my work on.
So my question to you guys is, how would I show that equality in Mathematica?
 
Physics news on Phys.org
How come that there is no gamma dependence in you derivation?
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 19 ·
Replies
19
Views
3K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
5
Views
2K
Replies
12
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K