Exercise · ZW-TIME-DERIVATIVE-003 · ★★☆ Intermediate
The equality \(\dot{\varphi}_t=v_t\circ\varphi_t\) is a form of...
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- D. A differential equation relating velocity to the current position
Explanation
The equality \(\dot{\varphi}_t=v_t\circ\varphi_t\) fixes the derivative in terms of the field evaluated at the current position, so it is a differential equation. It defines the flow from \(v_t\).
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?
- ZW-TIME-DERIVATIVE-002 If φ_t=0 for all t, what happens to the flow?
- 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?