# Introduction to Tensor Calculus, 2D force-free Motion problem

1. Jun 3, 2014

### CiaraB

Hi everyone,

I'm having a little trouble understanding something, hopeful I'm missing something very obvious!

It's an example of tensors being used to write multiple equations as one thing, so it's 2D force-free motion and we can write that in two ways;

1) $\ddot{x}$=0, $\ddot{y}$=0

2) $\ddot{r}$=r$\dot{θ}$$^{2}$, $\ddot{θ}$=$\frac{-2}{r}$$\dot{r}$$\dot{θ}$

Apparently both of these can be written as the vector equation;

$\ddot{X}$=0

Clearly the first equations can be written as this, but I don't quite see how it works for the second......surely if they can be written in that form they should be;

$\ddot{r}$=0 $\ddot{θ}$=0

I think my problem is less with tensors and more with the equations used.
Any help would be much appreciated!