# Unknown expression

1. Nov 17, 2013

### intervoxel

Hi,

I'm reading a paper on foundations of QM where the expression below appeared

$\frac{1}{2}m\left(\frac{d^2 \overrightarrow{r}^2}{dt^2}\right)=m\left(\frac{d^2 \overrightarrow{r}}{dt^2}\right).\overrightarrow{r}+m\left(\frac{d \overrightarrow{r}}{dt}\right)^2$

I cannot identify where it came from. Can you help me?

Last edited: Nov 17, 2013
2. Nov 17, 2013

### ZapperZ

Staff Emeritus
This is not sufficient for our forum. You must make proper citation to your source, as if you're citing it in a paper (i.e. author, journal, volume, pg number, year).

Yes, we may be just a public forum, but we require such level of citation whenever possible.

Zz.

3. Nov 17, 2013

### George Jones

Staff Emeritus
From

\begin{align} \frac{1}{2} m \frac{d}{dt} \frac{d}{dt} \left( \mathbf{r} \cdot \mathbf{r} \right) &= \frac{1}{2} m \frac{d}{dt} \left( \frac{d \mathbf{r}}{dt} \cdot \mathbf{r} + \mathbf{r} \cdot \frac{d \mathbf{r}}{dt} \right)\\ &= m \frac{d}{dt} \left( \frac{d \mathbf{r}}{dt} \cdot \mathbf{r} \right)\\ &= m \frac{d^2 \mathbf{r}}{dt^2} \cdot \mathbf{r} +m \frac{d \mathbf{r}}{dt} \cdot \frac{d \mathbf{r}}{dt} \end{align}

4. Nov 17, 2013

### intervoxel

O.k.

A New Stochastic Model of the Causal Interpretation of Quantum Theory on the Development of the Fundamental Concept of Mass
arXiv.org > quant-ph > arXiv:1311.1836