Poisson Equation on a Circular Membrane
 The static solution (Green's function) for the Poisson equation for a single force applied on a circular thin membrane at the point (  ,  ) is called the Green's function for the circular membrane, which is parameterized by ( ,  ). Poisson's equation for the Green's function  isand the Green's function for the Dirichlet boundary condition, when the circular boundary at radius  is held to zero displacement, is given by (for  )This solution is, with some manipulation, from Duffy, eq. 5.2.36. Because the solution has no series summation, like many Green's functions for the Poisson equation, it can be computed rather rapidly. The solution depends on  and on the angular difference  in such a way that there is little value in enabling the viewer to manipulate  , but this is provided anyway. The user can cut  off at any arbitrary positive value.  "Poisson Equation on a Circular Membrane" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/PoissonEquationOnACircularMembrane/ Contributed by: David von Seggern (University Nevada-Reno) | ||||||||||||||
  
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