All Questions
Tagged with differentiation velocity
105 questions
3
votes
3
answers
2k
views
Physical Meaning of Divergence of Convective Velocity Term
When taking the divergence of the convective velocity term, I get the following:
\begin{align}
\nabla\cdot\left[\mathbf u\cdot\nabla\mathbf u\right]&=\frac{\partial}{\partial x_i}\left[u_j\frac{\...
- 379
5
votes
4
answers
5k
views
How can there be really any instantaneous velocity?
I have read about Zeno's arrow paradox that tells us there is no motion of the arrow at a particular instant of its flight. It can be inferred that there can be no velocity at any instant. Moreover we ...
user36790
1
vote
4
answers
6k
views
When we take time derivative of a function of time, then is the result another function of time, again?
(I'll try to explain my question by one known example), for example where the velocity is a function of time v(t) then its time derivative (which is acceleration: $a=\frac {dv}{dt}$) is another ...
- 21
-8
votes
3
answers
385
views
Is there any other mathematical tool to measure velocity, instead useing derivative? [closed]
To measure velocity we use derivative
$$v=\frac {dr}{dt}.$$
Is the any other mathematical tool to do this?.
- 19
15
votes
2
answers
4k
views
Why does cancellation of dots $\frac{\partial \dot{\mathbf{r}}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$ work?
Why is the following equation true?
$$\frac{\partial \mathbf{v}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$$
where $\mathbf{v}_i$ is velocity, $\mathbf{r}_i$ is the ...
- 1,483