- #1

Arman777

Gold Member

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## 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.

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.