{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 243 "# drumhead problem, General case, Example 3 in Asmar 4.3\n# u_\{tt\} = c^2(laplacian u), \+ u=0 on clamped edge\n# circle radius=a, c=wave speed, \n# position = f (r,theta) = (a^2-r^2)*r*sin(theta),\n# velocity = g(r,theta) = (a^2-r^ 2)*r^2*sin(2*theta) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "a:= 1;c:=1;N:=5;\nf:=(r,theta)->(a^2-r^2)*r*sin(theta);\ng:=(r,theta)->(a^ 2-r^2)*r^2*sin(2*theta);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "alpha1:=evalf([BesselJZeros(1,1..N)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "b1:=n->2*2*(a^5)*4/(alpha1[n]^3*BesselJ(2,alpha1[n])) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "u1:=(r,theta,t)->sin(t heta)*sum(b1(n)*BesselJ(1,alpha1[n]*r)*cos(alpha1[n]*c*t),n=1..N);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "alpha2:=evalf([BesselJZeros (2,1..N)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "b2star:=n->2 4/(alpha2[n]^4*BesselJ(3,alpha2[n]));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "u2:=(r,theta,t)->sin(2*theta)*sum(b2star(n)*BesselJ(2 ,alpha2[n]*r)*sin(alpha2[n]*c*t),n=1..N);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 44 "u:=(r,theta,t)->u1(r,theta,t)+u2(r,theta,t);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "addcoords(z_cylindrical,[z,r ,theta],[r*cos(theta),r*sin(theta),z]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "plot3d(f(r,theta),r=0..a,theta=0..2*Pi,coords=z_cylin drical,orientation=[13,81]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "plot3d(g(r,theta),r=0..a,theta=0..2*Pi,coords=z_cylindrical);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "plots[animate](plot3d,\n[ u(r,theta,t),r=0..a,theta=0..2*Pi,coords=z_cylindrical,orientation=[13 ,81]],t=0..3.1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "# b1 ca n also be defined by integration directly." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 150 "b2:=n->(2/(Pi*BesselJ(2,alpha1[n])^2))*\nint(int(f (r,theta)*BesselJ(1,alpha1[n]*r)*r*sin(theta),theta=0..2*Pi),r=0..a); \nseq(evalf(b2(j)-b1(j)),j=1..N);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "16" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }