Exercise · ZW-TIME-DERIVATIVE-002 · ★★☆ Intermediate
If \(\dot{\varphi}_t=0\) for all \(t\), what happens to the flow?
Choose one option.
Show answer
- A. It stays constant in time; with \(\varphi_0=\operatorname{id}\), it remains the identity
Explanation
If the time derivative is zero, \(\varphi_t\) does not change and stays at \(\varphi_0\). With \(\varphi_0=\operatorname{id}\), the flow is the identity at all times.
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
- ZW-TIME-DERIVATIVE-001 In the LDDMM equation, what does φ_t represent?
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- ZW-TIME-DERIVATIVE-004 What is the difference between φ_t and an acceleration?
- ZW-TIME-DERIVATIVE-005 What is the initial condition of the flow φ_t in an initial value problem?
- ZW-TIME-DERIVATIVE-006 What is the time derivative of φ_t?
- ZW-TIME-DERIVATIVE-007 How is the time derivative of φ_t written?
- ZW-TIME-DERIVATIVE-008 What does the order of a time derivative indicate?
- ZW-TIME-DERIVATIVE-009 What is the flow φ_t in LDDMM?