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Conversions between vectors

  1. Jan 20, 2014 #1
    Given a vector ##d\vec{r}=dx\hat{x}+dy\hat{y}+dz\hat{z}## and another in its generalized form ##d\vec{q}=h_1dq_1\hat{q_1}+h_2dq_2\hat{q_2}+h_3dq_3\hat{q_3}##, being that dr = dq. How I do for connect the informations of one with another?

    The coordinates I know how do:
    [tex]\\d\vec{r}=\frac{d\vec{r}}{d\vec{q}}d\vec{q} \\ \begin{bmatrix} dx\\ dy\\ \end{bmatrix} = \begin{bmatrix} \frac{\mathrm{d} x}{\mathrm{d} q_1} & \frac{\mathrm{d} x}{\mathrm{d} q_2}\\ \frac{\mathrm{d} y}{\mathrm{d} q_1} & \frac{\mathrm{d} y}{\mathrm{d} q_2}\\ \end{bmatrix} \begin{bmatrix} dq_1\\ dq_2\\ \end{bmatrix}[/tex]

    But, I don't know how convert the basis and scale factor. Someone could explain me?
  2. jcsd
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