{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" } {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 "" 0 1 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 }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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Motion of a rod subjected \+ to the gravitation force only is given by:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "solv e(\{vdot*cos(theta)-v*thetadot*sin(theta)=0, vdot*sin(theta)+v*thetado t*cos(theta)=-1\},\{vdot,thetadot\});" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%)thetadotG,$*&-%$cosG6#%& thetaG\"\"\"%\"vG!\"\"!\"\"/%%vdotG,$-%$sinGF*F/" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 90 "But, as we introduce lift and drag forces (and the rod becomes glider), the equations are:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 170 "solve(\{vdot*cos(theta)-v*thetadot*sin(theta)=-v^2*s in(theta)-R*v^2*cos(theta), vdot*sin(theta)+v*thetadot*cos(theta)=-1+v ^2*cos(theta)-R*v^2*sin(theta)\},\{vdot,thetadot\});" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%%vdotG,&- %$sinG6#%&thetaG!\"\"*&%\"RG\"\"\")%\"vG\"\"#\"\"\"F+/%)thetadotG,$*&, &-%$cosGF)F.*$F/F2F+F2F0!\"\"F+" }}}{PARA 0 "" 0 "" {TEXT -1 1 " " } {MPLTEXT 1 0 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 40 "thetadot:=(theta,v)->(v^2-cos(theta))/v;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)thetadotGR6$%&thetaG%\"vG6\"6$%)operatorG %&arrowGF)*&,&*$)9%\"\"#\"\"\"\"\"\"-%$cosG6#9$!\"\"F3F1!\"\"F)F)F)" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "vdot:=(theta,v)->-sin(thet a)-R*v^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%vdotGR6$%&thetaG%\"vG6 \"6$%)operatorG%&arrowGF),&-%$sinG6#9$!\"\"*&%\"RG\"\"\")9%\"\"#\"\"\" F2F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "R:=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "?fieldplot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "fieldplot([thetadot,vdot],-Pi..Pi,.2..3);" }}{PARA 13 "" 1 "" {INLPLOT "6#-%'CURVESG6\\dl7%7$$!1uwNN'RpI$!#:$\"1********* *****>!#;7$$!11>#=nXi(HF*$\"1,++++++?F-7$$!1Tp9:I%y/$F*$\"1!z:j_5U=#F- 7%7$$!1FP?/DGmHF*$\"1y#4,?Uw*=F-7$$!1>V!f([^bEF*$\"1A2*)*zdB5#F-7$$!1q bC+.aGFF*$\"1#3*3(GY6B#F-7%7$$!1!)z4d5m1EF*$\"1()Q$puYE\"=F-7$$!1J&QfR [PN#F*$\"18h1`KN(=#F-7$$!1QJB'3;!>CF*$\"1SoUl*4rC#F-7%7$$!1kgv\\,CJAF* $\"1`>50\"eow\"F-7$$!18*3iP\"yn?F*$\"1Z!)*[*=9LAF-7$$!1&e=&o/D;@F*$\"1 f,PW>CBAF-7%7$$!1Ko7Fu\"*[=F*$\"1)RicSzbz\"F-7$$!14mwrhr)y\"F*$\"1-wL% f?W?#F-7$$!1nAT%4=K\"=F*$\"1t#fi_Q%\\@F-7%7$$!1#yCj*=0&[\"F*$\"1V'\\p; 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