Laplacian Lecture Note | Lecture Note - Edubirdie

University:
Santa Fe College
Course:
ETS 2527C | Electromechanical Components and Mechanisms
Academic year:

2024
Views:

146

Pages:

2
Author:

Jabin F.

# Laplacian ∇^2 ∇²(∇s) = ∇²s → scalar Laplacian ∇²s = 1/fgh * [ ∂/∂u(f * ∂s/∂u) + ∂/∂v(g * ∂s/∂v) + ∂/∂w(h * ∂s/∂w) ] ∇²s = fgh + ∂/∂w(f * g * ∂s/∂w) Laplacian defined for both scalar and vector. A = Au*û + Av*v̂ + Aw*ŵ ∇²A = (∇²Au)*û + (∇²Av)*v̂ + (∇²Aw)*ŵ ∇²A = (y² + z²) * r̂ # eqn A = (x² + β³) * (y² + z²) * n̂ Ax = (y² + z²) ∇²A = (∇²Ax) * n̂ = (∂²/∂x² + ∂²/∂y² + ∂²/∂z²) * (y² + z²) * n̂ = (2 + 2) = 4 * n̂

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