Register to reply

Laplace in polar coords

Share this thread:
dp182
#1
Jul23-11, 06:32 PM
P: 22
1. The problem statement, all variables and given/known data
solve the polar coord equation


2. Relevant equations
Urr+(1/r)Ur+(1/r2)U[itex]\vartheta[/itex][itex]\vartheta[/itex]=0; 1[itex]\leq[/itex]r[itex]\leq[/itex]2, 0[itex]\leq[/itex][itex]\vartheta[/itex][itex]\leq[/itex][itex]\pi[/itex]/4
U(1,[itex]\vartheta[/itex])=0 U(2,[itex]\vartheta[/itex])=[itex]\vartheta[/itex]
U[itex]\vartheta[/itex](r,0)=0 U([itex]\vartheta[/itex],[itex]\pi[/itex]/4)=0
and has the form
U(r,[itex]\vartheta[/itex])=Uo(r,[itex]\vartheta[/itex])+[itex]\sum[/itex]cnRn(r)[itex]\vartheta[/itex]n([itex]\vartheta[/itex])

3. The attempt at a solution
so I used variation of parameters and the homogeneous boundaries with [itex]\vartheta[/itex] to get [itex]\vartheta[/itex]n([itex]\vartheta[/itex])=cos(4n[itex]\vartheta[/itex]) then taking r2R''+rR'-cR=0 and using the Euler equation to get r(r-1)+r-c which is r=[itex]\pm[/itex]c, c=16n2
so that will give me Rn(r)=Cnr4n+dnr-4n and knowing condition U(1,[itex]\vartheta[/itex])=0 bn=0 so whats left is Cnr4n I got stuck here how do I solve for Cn do I try subbing in conditions to solve or is there some equation im missing
and then using the
Phys.Org News Partner Science news on Phys.org
What lit up the universe?
Sheepdogs use just two simple rules to round up large herds of sheep
Animals first flex their muscles

Register to reply

Related Discussions
Seperable solutions of Laplace equation in circular polar coords Calculus & Beyond Homework 7
Change to Polar coords help Calculus & Beyond Homework 5
Can anyone help with cylindrical polar coords? Advanced Physics Homework 2
Polar coords of motion Introductory Physics Homework 5
Polar coords General Math 7