Taking the partial time derivative of a functional

  • I
  • Thread starter Arman777
  • Start date
  • #1
1,777
139

Main Question or Discussion Point

Let us suppose we have a functional of f such that ##f=f((\vec{r}(t),t)## where ##\vec{r}(t) = a(t)\vec{x}(t)##.

I am trying to derive an equation such that

$$\left.\frac{\partial}{\partial t}\right|_r = \left.\frac{\partial }{\partial t}\right|_x + \left.\frac{\partial \vec{x}}{\partial t}\right|_r \cdot \nabla_x $$

where ##\nabla_r = \frac{1}{a}\nabla_x##

It is actually about coordinate transformation.
 

Answers and Replies

  • #2
13,145
9,929
Your notation doesn't make any sense. Firstly, you wrote an equation of differential operators, not derivatives. Secondly, you evaluate an operator depending on one variable at a location of another variable. What does that mean? If it is only a coordinate transformation, then you need the chain rule, that's all.
 

Related Threads on Taking the partial time derivative of a functional

Replies
2
Views
3K
  • Last Post
Replies
5
Views
3K
Replies
2
Views
3K
Replies
7
Views
721
Replies
6
Views
4K
  • Last Post
2
Replies
25
Views
3K
Replies
10
Views
3K
Replies
2
Views
3K
Top