Bessel Functions and Normal Modes for a Disk C.G. (4-01) original version C.G. (5-07) .mw version Produce 1-D plots of the 1st 3 Bessel functions of the 1st and 2nd kind plus the normal modes for a disk. Clear the workspace. restart ; To plot in a separate window (must re-execute before each plotting command): plotsetup( window ) ; Plot the 1st 3 Bessel functions of the 1st kind. plot( [BesselJ(0,z),BesselJ(1,z),BesselJ(2,z)], z=0..15, -1..1, color=[red,green,blue], title="Bessel Functions of the 1st Kind", legend=["J0(z)","J1(z)","J2(z)"], numpoints=128 ); Plot the 1st 3 Bessel functions of the 2nd kind. plot( [BesselY(0,z),BesselY(1,z),BesselY(2,z)], z=0..15, -1..1, discont=true, color=[red,green,blue], title="Bessel Functions of the 2nd Kind", legend=["Y0(z)","Y1(z)","Y2(z)"], numpoints=128 ); Create z(r,theta) coordinate-plotting option ... found this in plot3d,coords help page. addcoords( zrtheta, [z,r,theta], [r*cos(theta),r*sin(theta),z] ); Set indices and appropriate Bessel-function zero for mode (m,n). m := 0; n := 1; zmn := evalf(BesselJZeros(m,n)): 'z[m,n]' = zmn;

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Name for the function to be plotted ... also used for coloring. z := BesselJ(m,zmn*r) * cos(m*theta) : Create a title string that identifies the indices of the mode. titlestring := cat( "m = ", m, " , n = ", n ): Surf plot of mode (m,n). plot3d( z, r=0..1, theta=0..2*Pi, coords=zrtheta, color=z, grid=[50,100], title=titlestring, titlefont=[TIMES,ROMAN,16] );