{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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{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$!\"\"F3F 1!\"\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "vdot:=(thet a,v)->-sin(theta)-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 82 "glider_eqs:=\{D(theta)(t)=thetadot(theta(t),v(t)) , D(v)(t)=vdot(thet a(t),v(t)) \};\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+glider_eqsG<$/- -%\"DG6#%&thetaG6#%\"tG*&,&*$)-%\"vGF,\"\"#\"\"\"\"\"\"-%$cosG6#-F+F,! \"\"F5F2!\"\"/--F)6#F3F,,&-%$sinGF9F;*&%\"RGF6F1F5F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "fixed_pt_eqns:= \{0=thetadot(theta,v) , 0 =vdot(theta,v) \};\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.fixed_pt_eq nsG<$/\"\"!*&,&*$)%\"vG\"\"#\"\"\"\"\"\"-%$cosG6#%&thetaG!\"\"F.F,!\" \"/F',&-%$sinGF2F4*&%\"RGF/F+F.F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "solve(fixed_pt_eqns,\{theta,v\});" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#<$/%\"vG-%'RootOfG6#,&-F'6#,&!\"\"\"\"\"*&)%#_ZG\"\"# \"\"\",&*$)%\"RGF2F3F.F.F.F.F.F-*$F0F3F./%&thetaG-%'arctanG6$,$*&F7F.F *F.F-F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "solve( \{0=theta dot(theta,v) , 0=vdot(theta,v)\},\{theta,v\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"vG-%'RootOfG6#,&-F'6#,&!\"\"\"\"\"*&)%#_ZG\"\"#\" \"\",&*$)%\"RGF2F3F.F.F.F.F.F-*$F0F3F./%&thetaG-%'arctanG6$,$*&F7F.F*F .F-F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "solve( \{0=v2 -cos (theta), 0=-sin(theta)-R*v2\},\{theta,v2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%&thetaG,$-%'arctanG6#%\"RG!\"\"/%#v2G*&\"\"\"F/*$-% %sqrtG6#,&*$)F*\"\"#F/\"\"\"F8F8F/!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {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 0 "" }}}}{MARK "11 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }