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Consider the motion p(a, t) given by p(x, t) = ((1+t)α₁, a2 + ta3, -ta₂+ α3)² and let f(x, t) = tx₁ + ₂ be an Eulerian scalar field. Compute the material time derivative of f in two ways: Df af + (v. V)ƒ_ and Df = f(p(ax, t), t)]la=$(z,t) - Ət Conclude that these quantities agree but that D[(x, t)/(x, t). 31.

Consider the motion p(a, t) given by p(x, t) = ((1+t)α₁, a2 + ta3, -ta₂+ α3)² and let f(x, t) = tx₁ + ₂ be an Eulerian scalar field. Compute the material time derivative of f in two ways: Df af + (v. V)ƒ_ and Df = f(p(ax, t), t)]la=$(z,t) - Ət Conclude that these quantities agree but that D[(x, t)/(x, t). 31.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the motion p(a, t) given by Ф(а, t) — ((1+ t)a1,02 + toз, —toz + 03)" and let f(x,t) = tx1 +x2 be an Eulerian scalar field. Compute the material time derivative of f in two ways: Df _ ðf Df dt d + (v · V)ƒ and Dt %3D b(x,t)• Dt Conclude that these quantities agree but that (r, t) + (x,t).
Transcribed Image Text:Consider the motion p(a, t) given by Ф(а, t) — ((1+ t)a1,02 + toз, —toz + 03)" and let f(x,t) = tx1 +x2 be an Eulerian scalar field. Compute the material time derivative of f in two ways: Df _ ðf Df dt d + (v · V)ƒ and Dt %3D b(x,t)• Dt Conclude that these quantities agree but that (r, t) + (x,t).
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