{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 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 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dot:=proc(r,q) simpl ify(add(r[i]*q[i],i=1..3)) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "cross:=proc(r,q) simplify([r[2]*q[3]-r[3]*q[2],r[3]*q[1]-r[1]* q[3],r[1]*q[2]-r[2]*q[1]]) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "mag:=proc(q) simplify(sqrt(add(q[i]^2,i=1..3))) end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "scalm:=proc(v,s) [seq(simpli fy(s*v[i]),i=1..3)] end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "grad:=proc(f) simplify([diff(f,x),diff(f,y),diff(f,z)]) end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "div:=proc(g) simplify(diff(g [1],x)+diff(g[2],y)+diff(g[3],z)) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "curl:=proc(g) simplify([diff(g[3],y)-diff(g[2],z),di ff(g[1],z)-diff(g[3],x),diff(g[2],x)-diff(g[1],y)]) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "plugin:=proc(g,r) simplify(eval(g, \{x=r[1],y=r[2],z=r[3]\})) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "findf:=proc(g) local h;h:=int(g[1],x);h:=h+int(g[2]-diff(h,y), y);h+int(g[3]-diff(h,z),z) end:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Type I integral:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f:=x*y^2*z^3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "r:=[cos(t),sin(t),t]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "rd:=diff(r,t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "int (plugin(f,r)*mag(rd),t=0..2*Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$ **\"\")\"\"\"\"\"$!\"\"\"\"##F&F)%#PiGF)F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Length:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "L:=int(mag(rd),t=0..2*Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG,$*(\"\"#\"\"\"F'#F(F'%#PiGF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Center of mass:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "[int(r[1]*mag(rd),t=0..2*Pi)/L, int (r[2]*mag(rd),t=0..2*Pi)/L, int(r[3]*mag(rd),t=0..2*Pi)/L];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"!F$%#PiG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Moment of inertia with respect to axis defined by:" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "a:=[3,0 ,-2]: b:=[1,2,-3]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "dsq :=dot(r-a,r-a)-dot(r-a,b)^2/mag(b)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dsqG,,\"#9\"\"\"*&\"\"'F'-%$cosG6#%\"tGF'!\"\"*&\"\"%F'F-F'F'*$) F-\"\"#F'F'*&#F'F&F'*$),*\"\"*F.F*F'*&F3F'-%$sinGF,F'F'*&\"\"$F'F-F'F. 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" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"!F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f:=findf(g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,(%\"xG \"\"\"*$)%\"yG\"\"#F'F'*$)%\"zG\"\"$F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "plugin(f,[1,0,2*Pi])-plugin(f,[1,0,0]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,$*&\"\")\"\"\")%#PiG\"\"$F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "int(dot(plugin(g,r),rd),t=0..2*Pi); # to \+ verify" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\")\"\"\")%#PiG\"\"$F& F&" }}}}{MARK "44" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }