{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 128 0 128 1 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 11 0 128 128 1 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "proj.ms " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 109 "Projectile motion i n Lagrangian formalism, to show how to make Maple do what it doesn't n aturally want to do." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 62 "Maple seems to need a lot of shifting around in the var iables." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "alias(x1=x1(t),y1=y1(t)):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 44 "L := m/2*(diff(x1,t)^2+diff(y1,t)^2)-m*g*y1; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG,&*&%\"mG\"\"\",&*$-%%diffG6 $%#x1G%\"tG\"\"#F(*$-F,6$%#y1GF/F0F(F(#F(F0*(F'F(%\"gGF(F4F(!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 74 "Lsvel:=subs(diff(x1,t)=vx1,diff(y1,t)=vy1,L); # L w ith symbolic velocities" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&LsvelG,& *&%\"mG\"\"\",&*$%$vx1G\"\"#F(*$%$vy1GF,F(F(#F(F,*(F'F(%\"gGF(%#y1GF(! \"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "px1:=diff(Lsvel,vx1 ); py1:=diff(Lsvel,vy1); # generalized momenta w/ symbols (pj = dLdqjd ot)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$px1G*&%\"mG\"\"\"%$vx1GF'" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$py1G*&%\"mG\"\"\"%$vy1GF'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 88 "px1a:=subs(vx1=diff(x1,t),px1); py1a:=subs(vy1=diff (y1,t),py1); # generalized p's 'live'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%px1aG*&%\"mG\"\"\"-%%diffG6$%#x1G%\"tGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%py1aG*&%\"mG\"\"\"-%%diffG6$%#y1G%\"tGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "La:=subs(x1=a,y1=b,L); # symbol sub s for lagrangian" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#LaG,&*&%\"mG\" \"\",&*$-%%diffG6$%\"aG%\"tG\"\"#F(*$-F,6$%\"bGF/F0F(F(#F(F0*(F'F(%\"g GF(F4F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "dLdx:= diff (La,a);dLdy:=diff(La,b); # derivatives wrt to symbolic coordinates (dL dqj)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dLdxG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dLdyG,$*&%\"mG\"\"\"%\"gGF(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "dLdxa:=subs(a=x1,b=y1,dLdx);dLdya:= subs(a=x1,b=y1,dLdy); # dL/dqj restored 'live'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&dLdxaG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&dL dyaG,$*&%\"mG\"\"\"%\"gGF(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "eqx:= diff(px1a,t)-dLdxa = 0;eqy:= diff(py1a,t)-dLdya = 0; # e quations of motion" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqxG/*&%\"mG \"\"\"-%%diffG6$-F*6$%#x1G%\"tGF/F(\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqyG/,&*&%\"mG\"\"\"-%%diffG6$-F+6$%#y1G%\"tGF0F)F)*&F(F)%\"g GF)F)\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "eqxa:=subs(x1 =a(t),y1=b(t),eqx);eqya:=subs(x1=a(t),y1=b(t),eqy); # new set of named vars" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqxaG/*&%\"mG\"\"\"-%%diff G6$-F*6$-%\"aG6#%\"tGF1F1F(\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% %eqyaG/,&*&%\"mG\"\"\"-%%diffG6$-F+6$-%\"bG6#%\"tGF2F2F)F)*&F(F)%\"gGF )F)\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "sol:=dsolve(\{e qxa,a(0)=0,D(a)(0)=10,eqya,b(0)=0,D(b)(0)=10\},\{a(t),b(t)\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG<$/-%\"aG6#%\"tG,$F*\"#5/-%\"bG F),&F*F,*&F*\"\"#%\"gG\"\"\"#!\"\"F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "assign(sol); x:=a(t); y:=b(t); # one more set of nam es for the plot " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG,$%\"tG\"#5 " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&%\"tG\"#5*&F&\"\"#%\"gG\" \"\"#!\"\"F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plot([x,sub s(g=98/10,y),t=0..2],title=`Projectile's path`);" }}{PARA 13 "" 1 "" {INLPLOT "6$-%'CURVESG6$7S7$\"\"!F(7$$\"1LLLL3VfV!#;$\"13$*46\"3jE%F,7 $$\"1nmm\"H[D:)F,$\"1y;zxW(o#yF,7$$\"1LLLe0$=C\"!#:$\"1?%)oWbEm6F77$$ \"1LLL3RBr;F7$\"1T:H#zvV`\"F77$$\"1nm;zjf)4#F7$\"1YnzZ^z#)=F77$$\"1LL$ e4;[\\#F7$\"14ReN[$)*=#F77$$\"1++]i'y]!HF7$\"1t'pF/W:\\#F77$$\"1LL$ezs $HLF7$\"1:_Oe8A'y#F77$$\"1++]7iI_PF7$\"1hSz=fRiIF77$$\"1nmm;_M(=%F7$\" 1[JXyg=GLF77$$\"1LLL3y_qXF7$\"1mEW58$pa$F77$$\"1+++]1!>+&F7$\"1\\*)[a \"pfx$F77$$\"1******\\Z/NaF7$\"1u$4(*)))f()RF77$$\"1+++]$fC&eF7$\"1\"G t#3m9uTF77$$\"1LL$ez6:B'F7$\"1WW,slvGVF77$$\"1mmm;=C#o'F7$\"1VEa(QwU\\ %F77$$\"1mmmm#pS1(F7$\"1/x06m\"*=YF77$$\"1****\\i`A3vF7$\"1v'*)eSEfu%F 77$$\"1lmmm(y8!zF7$\"1aWOK7AU[F77$$\"1,+]i.tK$)F7$\"1hw3$*\\WI\\F77$$ \"1,+](3zMu)F7$\"1fgP'=1v*\\F77$$\"1nmm\"H_?<*F7$\"1ZV&Gn^)\\]F77$$\"1 nm;zihl&*F7$\"13S&Rbm?3&F77$$\"1LLL3#G,***F7$\"1,a+*y(z*4&F77$$\"1LLez w5V5!#9$\"1v_#H+;&*4&F77$$\"1++v$Q#\\\"3\"F`s$\"1RYcMvv$3&F77$$\"1LL$e \"*[H7\"F`s$\"1mTBZ#>00&F77$$\"1+++qvxl6F`s$\"1%)fp?F\\)*\\F77$$\"1++] _qn27F`s$\"1q!Qcf*>I\\F77$$\"1++Dcp@[7F`s$\"1Hp8qiuZ[F77$$\"1++]2'HKH \"F`s$\"1T%)>oiKPZF77$$\"1nmmwanL8F`s$\"1qD14C<@YF77$$\"1+++v+'oP\"F`s $\"1ry'fyc%zWF77$$\"1LLeR<*fT\"F`s$\"1$)*[Oid_L%F77$$\"1+++&)Hxe9F`s$ \"1HvM.'Q/;%F77$$\"1mm\"H!o-*\\\"F`s$\"13,W&Qp&zRF77$$\"1++DTO5T:F`s$ \"1ftV!HMNx$F77$$\"1nmmT9C#e\"F`s$\"1\\B+;LKbNF77$$\"1++D1*3`i\"F`s$\" 1+d*Gw1\"4LF77$$\"1MLL$*zym;F`s$\"1]X?\"3(yaIF77$$\"1LL$3N1#4Z/?#F77$$\"1nm;9@BM=F`s$\"1)4HLkCn&=F77$$\"1LLL`v&Q(=F`s$\"1S)Ha 4**H`\"F77$$\"1++DOl5;>F`s$\"1Kh-(\\!*3<\"F77$$\"1++v.Uac>F`s$\"1O;%[` C#z!)F,7$$\"#?F($\"1')************RF,-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(- %&TITLEG6#%2Projectile's~pathG" 2 285 285 285 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 2 "" 1 "" {TEXT -1 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "16 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }