ondas-circulo.html

VIBRACIONES DE UNA MEMBRANA CIRCULAR

Solución de u_{tt}(x,y,t) =u_{xx}(x,y,t)+u_{yy}(x,y,t),     si x^2+ y^2 < 1 y t en (0,10],

u(x,y,t)=0,     si x^2+y^2 = 1 y t en (0,10],

u(x,y,0)=1-(x^2+y^2),    si x^2+ y^2 <= 1,

u_t(x,y,0)=0,    si x^2+ y^2 < 1,

usando series de Fourier-Bessel.

> z:=4*sum('BesselJ(0,BesselJZeros(0,n)*r)*BesselJ(2,BesselJZeros(0,n))/((BesselJZeros(0,n))^2*(BesselJ(1,BesselJZeros(0,n)))^2)*cos(BesselJZeros(0,n)*t)','n'=1..6):
animate(plot3d,[[r,theta,z],theta=0..2*Pi,r=0..1,coords=cylindrical],t=0..10);