Search results with tag "In the polar coordinate system"

Laplace’s equation in the Polar Coordinate System

represent the heat and wave equations in the polar coordinate system. For the heat equation, the solution u(x,y t)˘ r µ satisfies ut ˘k(uxx ¯uyy)˘k µ urr ¯ 1 r ur ¯ 1 r2 uµµ ¶, k ¨0: diffusivity, whereas for the wave equation, we have utt ˘c 2(u xx ¯uyy)˘c 2 µ urr ¯ 1 r ur ¯ 1 r2 uµµ ¶ c ¨0: wave velocity. 3

  System, Coordinates, Equations, Waves, Velocity, Polar, Wave velocity, Equation in the polar coordinate system, In the polar coordinate system