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

  1. Jun 3, 2014 #1
    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) [itex]\ddot{x}[/itex]=0, [itex]\ddot{y}[/itex]=0

    2) [itex]\ddot{r}[/itex]=r[itex]\dot{θ}[/itex][itex]^{2}[/itex], [itex]\ddot{θ}[/itex]=[itex]\frac{-2}{r}[/itex][itex]\dot{r}[/itex][itex]\dot{θ}[/itex]

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

    [itex]\ddot{X}[/itex]=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;

    [itex]\ddot{r}[/itex]=0 [itex]\ddot{θ}[/itex]=0

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

    Thank-you in advance
     
  2. jcsd
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