- #1
mjordan2nd
- 177
- 1
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.
\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.