Hi, I going through my class notes for a fluids class, specifically fundamental solutions of the Stokes equations. To derive the stresslet and rotlet involves solving the following
ui = (1/8*pi*μ)*(∂Gik/∂xj)*Fk*Aj
Gik(x) = δij*(1/r)+(xixj/r3)
We looked at it in a lecture (skipping all the "easy parts"!! of course) and I am trying to fill in the gaps. The first step is to taylor expand it at A/2 wit |A/2| << |x|.
This should give ui(x) = (1/8*pi*μ)*(Gik(x-0)Fk + (Ai/2)*∂/∂xj(Gik)(x - 0)*Fk + ... (Mix of vector and suffix notation here very confusing)
Then do the same at -A/2 (with -F) and add the solutions
Taylor series: f(a) + f'(a)*(x-a) + (f''(a)/2!)*(x-a)2 + ....
The Attempt at a Solution
My problem is the mix of notation, I am not sure how to apply the taylor series here. Any help appreciated.