# Galilean transform

1. Jan 21, 2013

### MarkovMarakov

1. The problem statement, all variables and given/known data
If there is a change of variables:
$$(\vec x(t),t)\to (\vec u=\vec x+\vec a(t),\,\,\,v=t+b)$$ where $b$ is a constant.

Suppose I wish to write the following expression in terms of a gradient in $(\vec u, v)$

$$\nabla_\vec x f(\vec x,t)+{d^2\vec a\over dt^2}$$ How do I do that?

2. Relevant equations

3. The attempt at a solution
For the first term, I think
$$f(\vec x, t)\to f(\vec u -\vec a, v-b)$$
I am not sure what to do with the second term though.

2. Jan 22, 2013

### CFede

You should use chain rule I think, so

$\frac{\partial }{\partial x}=\frac{\partial u}{\partial x}\frac{\partial}{\partial u}$

If I understood your question, this is what you are looking for.