Equations in Polar Coordinates

Velocity Components:

$$v_r = {{\partial \phi} \over {\partial r}} = {1 \over r} {{\partial \psi} \over {\partial \theta}}$$

$$v_\theta = {1 \over r} {{\partial \phi} \over {\partial \theta}} = - {{\partial \psi} \over {\partial r}}$$ (4.69)

Laplacian:

$${{\partial^2 \phi} \over {\partial r^2}} + {1 \over r}{{\partial ... ...ver {\partial r}} + {1 \over r^2}{{\partial^2 \psi} \over {\partial \theta^2}}$$ (4.70)

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney