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Unknown expression

  1. Nov 17, 2013 #1
    Hi,

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

    [itex]
    \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
    [/itex]

    I cannot identify where it came from. Can you help me?
     
    Last edited: Nov 17, 2013
  2. jcsd
  3. Nov 17, 2013 #2

    ZapperZ

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    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.
     
  4. Nov 17, 2013 #3

    George Jones

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    From

    $$\begin{align}
    \frac{1}{2} m \frac{d}{dt} \frac{d}{dt} \left( \mathbf{r} \cdot \mathbf{r} \right) &= \frac{1}{2} m \frac{d}{dt} \left( \frac{d \mathbf{r}}{dt} \cdot \mathbf{r} + \mathbf{r} \cdot \frac{d \mathbf{r}}{dt} \right)\\
    &= m \frac{d}{dt} \left( \frac{d \mathbf{r}}{dt} \cdot \mathbf{r} \right)\\
    &= m \frac{d^2 \mathbf{r}}{dt^2} \cdot \mathbf{r} +m \frac{d \mathbf{r}}{dt} \cdot \frac{d \mathbf{r}}{dt}
    \end{align}$$
     
  5. Nov 17, 2013 #4
    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
    Muhamad Darwis Umar
    Eq. 14d
     
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