- #1

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## Main Question or Discussion Point

I am trying to self-study some physics, and have gotten a little stuck in one of Goldstein's derivations. The dot-notation is still confusing to me. Equation 1.51 in Goldstein states that

[tex]

\frac{\partial \vec{v_i}}{\partial \dot{q_j}} = \frac{\partial \vec{r_i}}{q_j}

[/tex]

I do not understand how he arrives at this equation. He states that this comes from equation 1.46, which is

[tex]

v_i = \frac{dr_i}{dt} = \frac{\partial r_i}{\partial q_k}\dot{q_k} + \frac{\partial r_i}{\partial t}

[/tex]

where the summation convention is implied, but I do not see how he goes from here to 1.51. Any help would be appreciated. Thanks.

[tex]

\frac{\partial \vec{v_i}}{\partial \dot{q_j}} = \frac{\partial \vec{r_i}}{q_j}

[/tex]

I do not understand how he arrives at this equation. He states that this comes from equation 1.46, which is

[tex]

v_i = \frac{dr_i}{dt} = \frac{\partial r_i}{\partial q_k}\dot{q_k} + \frac{\partial r_i}{\partial t}

[/tex]

where the summation convention is implied, but I do not see how he goes from here to 1.51. Any help would be appreciated. Thanks.