{VERSION 5 0 "APPLE_PPC_MAC" "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 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 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 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Normal" -1 256 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 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "g:=10;m:=1;k:=1;l_0:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"mG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$l_0G\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 159 " \013eqs:=diff(l(t),`$`(t,2)) = l(t)*diff(phi(t),t)^2-k/m*(l(t)-l_0)+g* cos(phi(t)),\ndiff(phi(t),`$`(t,2)) = -2/l(t)*diff(l(t),t)*diff(phi(t) ,t)-g/l(t)*sin(phi(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqsG6$/- %%diffG6$-%\"lG6#%\"tG-%\"$G6$F-\"\"#,**&F*\"\"\")-F(6$-%$phiGF,F-F1F4 F4F*!\"\"F4F4*&\"#5F4-%$cosG6#F8F4F4/-F(6$F8F.,&*(F*F:-F(6$F*F-F4F6F4! \"#*(F " 0 "" {MPLTEXT 1 0 46 "ics:=phi(0)=10,D(phi)(0)=0,l(0)=1.2,D(l)(0)=0;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$icsG6&/-%$phiG6#\"\"!\"#5/--%\"DG6#F(F)F*/-%\"lGF) $\"#7!\"\"/--F/6#F3F)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " soln:=dsolve(\{eqs,ics\},\{l(t),phi(t)\},type=numeric);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%solnGf*6#%(rkf45_xG6.%\"iG%/comp_soln_dataG%( odeprocG%&icvecG%(LR_caseG%\"YG%$valG%)outpointG%#ptG%*stop_procG%+sto p_arrayG%&cplexG6#%aoCopyright~(c)~2000~by~the~University~of~Waterloo. ~All~rights~reserved.GE\\s\"Q(complex6\"%&falseGC2@$-%'memberG6$9$7$Q4 left_comp_soln_dataF9Q5right_comp_soln_dataF9O\"\"!@$2%'DigitsG-%&trun cG6#-%'evalhfG6#FH>FHFI>8+-%&evalfG6#F@@$4-%%typeG6$FQ.%(numericG@%-F> 6$FQ7%Q&startF9Q%leftF9Q&rightF9O$FEFEO-.9!FT>8&f*6&%\"NG%\"tG%\"YG%#Y PGF96#%co[Y[1]~=~l(t),~Y[2]~=~diff(l(t),t),~Y[3]~=~phi(t),~Y[4]~=~diff (phi(t),t)]GF9C&>&9'6#\"\"\"&9&6#\"\"#>&F`pFep,**&&FdpFapFbp)&Fdp6#\" \"%FfpFbpFbpF[q!\"\"FbpFbp*&\"#5Fbp-%$cosG6#&Fdp6#\"\"$FbpFbp>&F`pFgqF ]q>&F`pF^q,&*(F[qF`qFcpFbpF]qFbp!\"#*(FbqFbpF[qF`q-%$sinGFeqFbpF`qF9F9 F9>8'=F96#;FbpF_qE\\[l%Fbp$\"#7F`qFfpF^oFhq$FbqFEF_qF^o>8-FE>8.FE>8)-% $mapG6$%$rhsG-%&parseG6#-%#opG6$Fhq-%%evalG6#Fdo>8/-Fbo6#F8@'/FQF^oO7$ /FhoFQ-%$seqG6$/&Fas6#8$-FS6#&FdrF]u/F^u;Fbp-%%nopsG6#Fas1F^oFQ>8(FC>F iuFB>8%-Fbo6#Fiu@%4-FX6$7#F\\v7#.%%listGC%Z%>F\\v-%;dsolve/numeric/SC/ IVPsolveG6)Fdo;F^oFQFdrF]sF_sF`t/%'scprocGF:F9C&@$/F`t%%trueGYF9>F`tFc w>F\\vFjv>FatFcw>8*&&F\\vFgq6#&F\\vFep>F]vF\\vC$>FiwFjw@$53/FiuFC2FiwF Q3/FiuFB2FQFiwC&@$5/&F\\v6#\"\")Fbp2FbqF]yC$>FiwFjw@%FdxY6$QQcannot~ev aluate~the~solution~further~right~of~%1F9-&FSF^y6#FiwY6$QPcannot~evalu ate~the~solution~further~left~of~%1F9FgyZ%>F\\v-%F`tFcw>F\\vF_z>FatFcw> F]vF\\v>FiwFjw@&FdxC$@$33/%:_Env_smart_dsolve_numericGFcw2F^oFiw2-Fbo6 #F\\oFiw>Fc[lFiw@$Fex@)/&F]vF^yFbpY6$Qcocannot~evaluate~the~solution~f urther~right~of~%1,~probably~a~singularityF9Fgy/Fi[lFfpY6$Qcqcannot~ev aluate~the~solution~further~right~of~%1,~maxfun~limit~exceeded~(see~?d solve,maxfun~for~details)F9Fgy2FbqFi[lC$@$0%7_Env_dsolve_nowarnstopGFc w-%(WARNINGG6#-_%,StringToolsG%.FormatMessageG6%Qhocannot~evaluate~the ~solution~further~right~of~%1,~stop~condition~#%2~violatedF9Fgy,&Fi[lF bpFbqF`q>FQFiwYFeyFgxC$@$33F_[l2FiwF^o2Fiw-Fbo6#F[o>Fh]lFiw@$Fhx@)Fh[l Y6$Qbocannot~evaluate~the~solution~further~left~of~%1,~probably~a~sing ularityF9FgyF]\\lY6$Qbqcannot~evaluate~the~solution~further~left~of~%1 ,~maxfun~limit~exceeded~(see~?dsolve,maxfun~for~details)F9FgyFa\\lC$@$ Fd\\l-Fg\\l6#-Fj\\l6%Qgocannot~evaluate~the~solution~further~left~of~% 1,~stop~condition~#%2~violatedF9FgyF_]l>FQFiwYF[z>Fiw-%9dsolve/numeric /SC/IVPvalG6$F\\vFQ7$Fgt-Fit6$/F\\u&FiwF]uFbuF9F9F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "soln(0.2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7'/%\"tG$\"\"#!\"\"/-%\"lG6#F%$\"3k3yd,Y[M5!# " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "7 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }