- #1
Maor Hadad
- 9
- 0
Homework Statement
[tex]v_{i}=\dot{x}_{i}=\dot{x}_{i}\left(q_{1},q_{2},..,q_{n},t\right)[/tex]
[tex]T \equiv \frac{1}{2}\cdot{\sum}m_{i}v_{i}^{2}[/tex]
[tex] \frac{\partial T}{\partial\dot{q}_{k}}={\sum}m_{i}v_{i}\frac{\partial v_{i}}{\partial\dot{q}_{k}}={\sum}m_{i}v_{i}\frac{\partial x_{i}}{\partial q_{k}}[/tex][/B]
Homework Equations
Why is it ok to assume:
[tex]\frac{\partial v_{i}}{\partial\dot{q}_{k}} = \frac{\partial x_{i}}{\partial q_{k}}[/tex]
The Attempt at a Solution
I can say that:
[tex]\frac{\partial x_{i}}{\partial q_{k}}=\frac{\partial x_{i}}{\partial t}\frac{\partial t}{\partial q_{k}}=\frac{v_{i}}{\dot{q_{i}}}[/tex] but it's not the same as written.
and the expression [tex]\frac{\partial v_{i}}{\partial\dot{q}_{k}}[/tex] says to differentiate the velocity according to change of the q quardinate in time.
Last edited: