Solving the Biharmonic Equation in Polar Coordinates: Tips and Techniques

[member 428835]

hey pf!

does anyone here have a link (or perhaps would care to share some info) on how to solve the biharmonic equation in polar coordinates (or, at least rectangular coordinates): $$ \nabla^4 \psi = 0$$ where $\psi = f(r,\theta)$

i should say i have already done the obvious searches but didnt understand wikipedia and wolfram simply gave the answer, which is great but curiosity still has me. does separation of variables really work here?

thanks!

 

[Chestermiller]

hey pf!

does anyone here have a link (or perhaps would care to share some info) on how to solve the biharmonic equation in polar coordinates (or, at least rectangular coordinates): $$ \nabla^4 \psi = 0$$ where $\psi = f(r,\theta)$

i should say i have already done the obvious searches but didnt understand wikipedia and wolfram simply gave the answer, which is great but curiosity still has me. does separation of variables really work here?

thanks!

See Transport Phenomena, by Bird, Stewart, and Lightfoot, example 4.2-1, p. 122.
Creeping Flow around a sphere.

 

[member 428835]

thanks chestermiller! ironically enough creeping flow around a sphere is the reason for my inquiry! i appreciate it!