ICXOdd   1Courier NewSymbolExtendedBxyx1Courier New1Courier NewTimes New RomanTimes New Romanxyx1Courier New1Courier New1Courier New1Courier NewIPDIPDIPDIPD { d< .22pˊ@ˊˢ@˖@˖??X?h!?@@@@@@033333??@^ߛOw????poL:@4 LPZPZ@@?@ @@@ GimN?@@ 2??@Nw!@???????|yz{|}~]hp\/.5(ka(r)+kb(r)+kc(r))*(t-sin(t))*h(theta(r)-t)11-.5(ka(r)+kb(r)+kc(r))*(1-cos(t))*h(theta(r)-t)(x,y) = (.5(ka(r)+kb(r)+kc(r))*(t-sin(t))*h(theta(r)-t),1-.5(ka(r)+kb(r)+kc(r))*(1-cos(t))*h(theta(r)-t)); 0.000000 <= t <= 6.283185OO2??@??????Нѝҝӝԝ՝֝8ܨzr-(r/4-1)*hvs(r-4)r0#seg (r,-(r/4-1)*hvs(r-4)) to (r,0)22??@???????g詭(Ԧ˫_0*hvs(1/sqrt(3)-r)1*hvs(1/sqrt(3)-r)r*hvs(1/sqrt(3)-r)0*hvs(1/sqrt(3)-r)Wseg (0*hvs(1/sqrt(3)-r),1*hvs(1/sqrt(3)-r)) to (r*hvs(1/sqrt(3)-r),0*hvs(1/sqrt(3)-r))QQ2??@??????ם؝ٝڝ۝ܝݝpm<`ײ$0*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r)$1*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r),1/sqrt(3)*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r)$0*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r)seg (0*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r),1*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r)) to (1/sqrt(3)*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r),0*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r))QQ2??@??????ċȌ̍贶d-dou.(1/sqrt(3))*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r)$0*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r)$r*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r)$0*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r)seg ((1/sqrt(3))*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r),0*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r)) to (r*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r),0*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r))QQ2??@??????ޝߝ|{Эֶ{0*hvs(r-2-sqrt(3))1*hvs(r-2-sqrt(3))!r*(2/sqrt(3)-1)*hvs(r-2-sqrt(3))$-(r*(2-sqrt(3))-1)*hvs(r-2-sqrt(3))vseg (0*hvs(r-2-sqrt(3)),1*hvs(r-2-sqrt(3))) to (r*(2/sqrt(3)-1)*hvs(r-2-sqrt(3)),-(r*(2-sqrt(3))-1)*hvs(r-2-sqrt(3)))QQ2??@??????Ўԏܑؐ䓡蔡@䁵tp!r*(2/sqrt(3)-1)*hvs(r-2-sqrt(3))$-(r*(2-sqrt(3))-1)*hvs(r-2-sqrt(3))r*hvs(r-2-sqrt(3))$-(r*(2-sqrt(3))-1)*hvs(r-2-sqrt(3))seg (r*(2/sqrt(3)-1)*hvs(r-2-sqrt(3)),-(r*(2-sqrt(3))-1)*hvs(r-2-sqrt(3))) to (r*hvs(r-2-sqrt(3)),-(r*(2-sqrt(3))-1)*hvs(r-2-sqrt(3)))QQ2??@??????@/-õr*hvs(r-2-sqrt(3))$-(r*(2-sqrt(3))-1)*hvs(r-2-sqrt(3))r*hvs(r-2-sqrt(3))0*hvs(r-2-sqrt(3))hseg (r*hvs(r-2-sqrt(3)),-(r*(2-sqrt(3))-1)*hvs(r-2-sqrt(3))) to (r*hvs(r-2-sqrt(3)),0*hvs(r-2-sqrt(3)))QQxyzJXT@@@@@@@@@@@@@@@@@@@K7A@@@@@@@@@n Ln Ln LPI+X-PI/8*X^2+(PI^2/32-1/6)X^3+(PI/12-5PI^3/512)*X^4TTWOT(7/120-5PI^2/128+7PI^4/2048)*X^5 8TTWOA(-311PI/5760+7PI^3/384-21PI^5/16384)*X^6-0.00374019394*X^7TTWOB.00223180547*X^8-.00096099957*X^9+.0002715983*X^10٭TTWOCPTTWO(X-PI/2)+TTWOA(X-PI/2)+TTWOC(X-PI/2)THETBHVS(X-PI/4)*HVS(PI-X)*THETB(X)X)THETAB2PI-2*SQRT(PI/X)-PI*SQRT(PI/X)/(3X)+2PI/(3X^2)TTHREEL(3X -9/10*X^3+729/1400*X^5)*HVS(PI/4-X)THETAATHETAA(X)+THETAB(X)+HVS(X-PI)*TTHREE(X)471(x-pi/2)^3-0.04099THETA-pi/4/(9X^2)+3/5+81/700*X^2-27/1400*X^4+22599/3080000*X^6t <= 6KASfWrH1+X^2/4-PI*X^3/16+.1510990443X^4-.1137821991X^5KBA.08402736939X^6-.06102302726X^7+.04369367357X^88@KBB-.03091563799X^9+.02165728736X^10KBCD(KBA(X-PI/2)+KBB(X-PI/2)+KBC(X-PI/2))KBSX/PI+2/(3SQRT(PI*X))+SQRT(PI/X)/(5X)2/(9X^2)KCSKA(X)+KB(X)+KC(X)KB(X-PI/2)+HVS(X)-PI/4)*KB(X-PI/2)K@KBS(X)*HVS(3PI/4-X)*HVS(X-PI/4)KBHVS(PI/4-X)*KAS(X)KAHVS(X-3PI/4)*KCS(X)KC<SQRT(X)/SQRT(ABS(X))Ha/La Max IuYA!QpMHM>@vI*$@GETATimes New RomanHub  Hk as a function of r = a/Lr = a/L 朗l<@b؊!@.Go?be԰|@Times New RomanHub Cycloid Path of Least Timee!U&|Pe?K6Z@zv/^Times New RomanHub "Left Ramp" Path of Least Time: Beta > 01Z?;@퐤"Z$]OpSTimes New RomanHub Y(x,y) = (.5(ka(r)+kb(r)+kc(r))*(t-sin(t))*h(theta(r)-t),1-.5sM1b@s*g@b'\@B6 (useg (r,-(r/4-1)*hvs(r-4)) to (r,0)/4-1)*hvs(r-4))?sM˖@˖ T0seg (0*hvs(1/sqrt(3)-r),1*hvs(1/sqrt(3)-r)) to (r*hvs(1/sqrtsM˖@˖ԣBfVseg (0*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r),1*hvs(r-1/sqrt(3))*sM˖@˖"S+Pseg ((1/sqrt(3))*hvs(r-1/sqrt(3))*hvs(2+sqrt(3)-r),0*hvs(r-1sM˖@˖de%seg (0*hvs(r-2-sqrt(3)),1*hvs(r-2-sqrt(3))) to (r*(2/sqrt(3)sM˖@˖"S+seg (r*(2/sqrt(3)-1)*hvs(r-2-sqrt(3)),-(r*(2-sqrt(3))-1)*hvssM˖@˖de%xseg (r*hvs(r-2-sqrt(3)),-(r*(2-sqrt(3))-1)*hvs(r-2-sqrt(3)))sM˖@˖"S+