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Ȍ̈̀Ȉ,,̀ ̂bL̈̌΢,<(,,, ,΢,̢̂΀ Ì̌.̂L̈,,Σ ̌΢, ̈,, ,,̈, 8̈,,,̂b,̂  <  ΌΈ,B̪ʈ ̈ĀB̪ʈȈψ,ΌȈ,Ȉ̈ ̀ ̪ʈ,Ό ̌L̬B̈̈( ̈.̌̌̌Ό̌  ḦȠ// ȈȌȈ(  ̌ ̌̌Œ̌  ̀̌ *.̈̈ ̈ ̈̀Ȉ̈Ḧ̈̄ .̈ȈĈ L𨨊* ``̌`̌ ̌̌``Έ,̌*/((⨂.⨂.興̈(ਂ...( 舠 ̀ 3333 Ȉ̌̌ ̌Ȉ̈̈̈L̈ ꂰ̈̈̌Œ`  ̀ ̌  .ό?RSRC LVINLBVWql qLD <@xZQlL3Mv ُ B~ ftչe,LVINBrachistochrone Trajectory.vi  @ Final X position@ Final Y Position @ Time@ a@ theta final @!Done@ Traversal Time&@P@ @ xy::P? c$ c P   c^P"@P@flg@oRt@eofudfP Final X positionx dfdP txdP oldP ext P   c^P"@P@flg@oRt@eofudfP Final Y Positionp dfdP txdP oldP ext P   cRP"@P@flg@oRt@eofudf P!Donex!dfdP!txdP!oldP!ext P   c\P"@P@flg@oRt@eofudfP Traversal Timex dfdP txdP oldP ext c RP"@P@flg@oRt@eofudf P Timex dfdP txdP oldP ext P   cNP"@P@flg@oRt@eofudfP ax dfdP txdP oldP ext P   cXP"@P@flg@oRt@eofudfP theta finalx dfdP txdP oldP ext4 P@@@  P   4 P@@@  P   cP"@P@flg@oRt@eofudf&PP@ @ xy&xP@ @ dfd&PP@ @ txd&PP@ @ old&PP@ @ ext c\! @ T($P@ @@ y@ @@ y@ y@ y@ Final Y Position c @ x@ Final X position @ Time @ a c@ q@ theta final c( c  c c c c c c c c c c c cT cD \^@$??@??6@4@P(* 0DtlHXt  @@J(@D@dH@rX@8@ @@0<(@  @,VIDSBrachistochrone Trajectory.vi | i386 @code,50p E{dE`ETPUEd$==Ð#Ӏ}#EPXC@C$({(tVW(H_^CDCLC,DC4HCT x_^ZY[]ÐQRu 蜍d$ZY%Ul$SQRVW}'uQRUqd$ZY_^ZY[]ÐUl$SQRVWt$$|$(SQRVWPEEXPE EXQRhhuhPED$XhRd$ZY=tMEEQRhhuhPED$XhqRd$ZY=t_^ZY[ÐuP$P$Fd$ _^ZY[]ÐUl$SQRVWuяFF@ېFDQRhUcd$ZY_^ZY[]ÐXa "  [  @G/ i   %J1BCODE,50p (6.0rc5Oldest compatible LabVIEW.0K0V0V0VpPPP@ Final X position@ Final Y Position @!Done@ Traversal Time @ Time@ a@ theta final&@P@ @ xy99ݽwp1 1`p     ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++DTHPDV088~&@ Final X position&@ Final Y Position @!Done6&@P@ @ xy  @ Traversal Time!@ y @ Time@ x@ T@ theta final@ q@ a@ @@ y0$P@ @@ y1$$<pppp0DDDXptXt<XXpp \Dj'{j({Final X positionHV0+W,W\D'(Final Y PositionHV0+W,WPD؈DoneZD  Traversal TimeHW0صضPD'E(ETimeHW0+W,WMD''/('/aHDM0-+>W-,>WWDV'gcV(gc theta finalHO0m+~Wm,~WNDxyN   HM0  N   HQ0$$N00 HQ06G6GN#4#4 HhM0:K:KMD xHDV0ararHDV0}c}dHDV0#4#4HDV0MD yHDW044HD$W0,4-4MD qHDK0 6 6NDw x qfMD TD++;q=t/sqrt(a); x=a*(q-sin(q)); y=-a*(1-cos(q)); T=qf*sqrt(a);MDwxaMDw}x}tHDO0,FPHPBrachistochrone Trajectory.vi lFPHPD908 d d k~,50 V050V0/ PH04XL\/47|@Pi|((\4 FH i&|10 H |&\do4  2H *X 1p 6H 0{'cp{'cp{'cp0H6|Pp 2H 'bq'bq'bqL :H *00zu0z/{.|-}@P͂ (4 lp 6 0'cp'cp'cp|4 F &14  2 *X1L : *00zu0z/{.|-}0  &\do04p 2 'bq'bq'bq4O0@PB(\h( X T$` (4 G<10 <* 2ø08?󟟏=租~yz~??<[~8{>܏øyY?<x>ϳq<ƿ1x0=}?x<ÿ?10 ?DD@?f"" c&""?f"" c&""?f"" c&""?f"" c&""?f"" c&""???窯YO8 >胀~臀~胀胀> DHĄHHHH̀ĠDH H ??K8 @ @  @ @ H Hࠏ  `8       `H ` ` `  ` ` ` `  ` H ` ` ?H `8 ` <  08̌b,,b.Ȉ,, È̌b.Ȉ,΢,̂. 8̈̈̌b,,fjfjf,, , ÌȈ̈,̂΢,,,,b,,b.̂.. 8̈̌b,,b.̂..Ƞ͡ʡʁ !̈̀Ȉ33 Hb̢̌̂b̈ ̈,̂Σ ̢̢̌.b.΀ Ìb,̂., ̈,,,Σ ̌΢,̢̢̌̂΀ Ì̌b,,,,,̂΢  < L Ό̬̌BB̪ʈȠ//ΌL̈( ̌B( Ȉ̈̌ (̈̀B HL,Ȉ ̌ȈȈḦ .Œ//  ̈̈LȈ ̌̌Œ̌ ̬Ȉ,̌ȈȈ (L/ ̈̀ .̈̌ ̌̌̄Ȉ̈̈̈̈̀̌Ό``̌ Ό̀Č ̌ ČȈ̎̌̌Č΢(̈̈̀̌̌Œ̌ ̈̌ȈḦ(̌ Ľ̌L Ȟ̌ČČ̌̌̈̀̌ (̈ H(̈̌̈̈Ĉ̌̌̌  ̌̌ ̈̀̈̀̌Č ̈̀ ̌̈ `Ḧ(̈ ̎ (̈̌̈̌̈(̈̌Ĉ(̈( ̈̈(̈̈Ľ//Œ̌Œ̌ΌȈ̈ ̌Ό /(̈/̈̎ H,̌̌Č̌̈̈̀ H̀̌̌ H(Ĉ L̈̀ ̀`( ̈ȞL ̌`̈ /(̈̌@*򨂏̀̌ Ȉ(̈̌̈̌̌̈̌L ̈(̌//Œ̌Œ̌ΌȈL ̈̌Ό Ľ. ̀̈ *̀ ̀Č (̈̀̌̌̈̀  ̀(*.(ਨ*. 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Find Brach@ a @ theta @!stop@! Propagate@!Stop Propagation@ Well Depth @ Time@ Brachistochrone Time@ Linear Time@ Well Time@ Deep Well Time?;Calculates the Brachistochrone curve extending between(0,0) and the Final X and Y positions entered above. The curve is defined by x=a*(theta-sin(theta)), y=a*(1-cos(theta). The program also propagates particles along the Brachistochrone curve and three other paths. Copyright Joel Fajans, U.C. Berkeley 2/6/200299ݽwp1 p1p0@++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++DTHPDtJ88x~XF6@@&P@@ x@@ yGraph&@ Final X position&@ Final Y Position@! Find Brach! @ theta@ a@ Y@ X8,( @ theta@ a@ Y@ X 4(@P@ @ DiskJ: (@P@ @ Disk@ a@ @ xc<0P@@ Input Element@ "@ Input Element2"P@ @ @ x@ y6&P@@ x@@ y@@ x@@ y0$P@@ x@ >.@$P@ @@ y6&P@@ xc@ *@milliseconds to wait(@millisecond timer value@ x1@ y1@ x3@ x2@ y2@ y3"@@ xcL@@P @!status @code@0sourceerror in (no error)(@@ Input ElementVF@p0@&P@@ x@@ y dup referenceRB@p0@&P@@ x@@ y referenceF6@P @!status @code@0source error out@ Active Plot@4@@PArray Constant&@Plot.Point Style*P(@Plot.Plot Interpolation @Plot.Plot Color @Plot.Line Width8,@"P@ @ &@p! reference @!stop@! Propagate@Disabled&@!Stop Propagation@ Well DepthN>P@@ Input Element@@ Input Element<0P@ @@ Input Element, @@ Final X positionRBP @@ Final X position@@ Input ElementXL@BP @@ Final X position@@ Input ElementTH@>P@@ Input Element@@ Input Element @ Time@ theta final @!Done @ Traversal Time6&@P@ @ xy  @ Final X position@ Final Y Position @ Time@ a@ theta final @!Done@ Traversal Time&@P@ @ xyP  &@P@ @ xy@ Traversal Time @!Done @ Time@ Final Y Position@ Final X positionX  &@P@ @ xy@ Traversal Time @!Done@ Well Depth @ Time@ Final Y Position@ Final X position\P@F@P @@ Final X position@@ Input Elementxy*@ Brachistochrone Time @ Deep Well Time@ Linear Time@ Well Time$@Plot.Fill/Pt. Color,  DDhh0@t@000000((00H0xx <x xxx  4HHH  H\4p\pHH000H00(0<lx\xxxx    X|X|XXXXXXXX         0 xxx( D ( 0((( X(  (00( (  (000 X   X X   (   h 0000xxxxx\l0xx Dx   ( \  ( D   (  D  D (  D  X ( ( ( (   xxl  44 QDrsGraphPD$    TimeHD$DE#:$:HDEU D$6wfHfU AmplitudeN0.\D**Final X positionHD\D**Final Y PositionHDVD   Find BrachH$4D'N'NQDthetaHtCMDaHA\DBO5BO5Stop PropagationPDananstopH$ Aw)w)UD)6*)6* PropagateH$@?L5?L5 H$@XeEXeEVD Well DepthHl@PDmzmzTimeHD@H @6MCy6NCyWD#0#0 Linear TimeH?6C6CUD#0)#0) Well TimeH?6C+6C+`D#0~#0~Brachistochrone TimeHT?6CG6CGZD#I0#J0Deep Well Time[D!b!bCalculates the Brachistochrone curve extending between(0,0) and the Final X and Y positions entered above. The curve is defined by x=a*(theta-sin(theta)), y=a*(1-cos(theta). The program also propagates particles along the Brachistochrone curve and three other paths.HDE%C&CHDDHUHUHDDkrxksxHDC RE00 True HDJQ'dR'd_D^k^kFind a and theta.vi[D#0#0BrachistochroneRDwxCenterMDbiciaMDxZDX%eiX&eiCreate Disk.viMDyMDbiciqDlm__xc=a*q;; x=xc-a*sin(q); y=-a+a*cos(q); x1=xc+a*sin(q); y1=-a-a*cos(q); x2=xc+a*cos(q); y2=-a+a*sin(q); x3=xc-a*cos(q); y3=-a-a*sin(q);HDPD ((ND(( HDK,~9,9HDA2?2?QD&o3&p3SpokeNDKXKXy2HD0K.;.?MD++xHD@K^zk^{k`DN,[N-[milliseconds to waitND  x1NDxcND3@3@x2ND""y1NDy3NDlylyx3QDmnSpoke`Dq~xq~xmilliseconds to waitQDGraphQD/1<P/2<PWheelVDde Edge pointHDK^w_w^DG4TG5TBrachistochrone.viREjfwjgw True ZD~7~8Array ConstantHDK 3!3VD#0(#0( Line WidthHDKLTMTQD  Color^DPlot InterpolationRD22Plot #WD  Point StyleHDLOWPWHDLNVOVHDL#P0X#Q0X`DYZmilliseconds to waitHD LNDQXRX UDpq PropagateHDDA6C6CHD@ UD&& PropagateUD PropagateHDpAjk HDTLTDDisabled^DEEBrachistochrone.vi^D""Brachistochrone.vi\D))Stop PropagationHD|LTDyzDisabled\DStop Propagation\DStop PropagationRE   True HDL:M;MHDL9F9FYDGTGT Input ElementHDLWdWdHDLrrMDT[U[xHDLUrVrNDQXRX HDL:M;MHDLUrVrHD@q~q~^DboboBrachistochrone.vi^DBrachistochrone.viUDvWvX PropagateHDM5B15B1YD%22%22 Input ElementHD M(,(,`D - -milliseconds to wait^DBrachistochrone.vi^DttBrachistochrone.viZDPPArray ConstantHDHMHDPM""HDXM%%HD`M"/$"3$HDhM_l&_p&RDPlot #^D  Plot InterpolationWD"/"/ Point StyleQDANANColorVD_l_l Line WidthQDlmGraphiDBrachistochrone Trajectory.viHDMTDnoDisabled`D/<`/<`Linear Trajectory.vi^DWWWell Trajectory.viHDMTDcdDisabled^DssBrachistochrone.vi^DWWWell Trajectory.viHDKd q:dq:MDT4a;T5a;x^DttBrachistochrone.vi^DXXBrachistochrone.vi^DBrachistochrone.vi^DuvBrachistochrone.vi^D*7*7Brachistochrone.vi^DBrachistochrone.vi\D>?Stop PropagationQD Xv YvGraphHDT@cpcpHD0 C W>@ :J!fmfm]v@O`40f` f @ :L!v]v]od@ :K!nenegl0 2-$%p4 3^  00 2(./q0 2(r0 2-s4 6" ;4@O@4vH  4 680  [ݳ0  kr>4 3^5vg<0 ALv4 $ @( 8 H@ P֬+84 F` +D0 ` do4  2` Hp 6` 0֠cp֠⼼cp֠▖cp0 @`p 2` ֬bq֬⼼bq֬▖bqL :` 0zu0z/{.|-}@ P l+ H( 

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