Exercise · ZW-TIME-DERIVATIVE-010 · ★★☆ Intermediate
If \(\dot{\varphi}_t=v_t\circ\varphi_t\) and \(v_t\) is zero, what happens to \(\varphi_t\)?
Choose one option.
Show answer
- A. \(\varphi_t\) does not change from \(\varphi_0\)
Explanation
If \(v_t=0\), then \(\dot{\varphi}_t=0\) and \(\varphi_t\) stays equal to \(\varphi_0\). The other options contradict that equation.
Review the concept: Time derivative
The time derivative \(\dot{\varphi}_t\) describes how a deformation changes as the time parameter \(t\) varies.
\[\dot{\varphi}_t=\frac{d\varphi_t}{dt}\]
More practice problems: time derivative
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