I9Odd   1Courier NewSymbolxyx1Courier New1Courier NewTimes New RomanTimes New Romanxyx1Courier New1Courier New1Courier New1Courier NewIPDIPDIPDIPD {  d< 7022ph!@h!@h!@??X?X?@@@@@@033333??@^ߛOw????poL:@4LPZPZ@@?@ @@@ rK-z{?@@ 2??@Nw!@???????}~ ɷ PyXϥzLjH.5(ka(r)+kb(r)+kc(r))*(t-sin(t))*sqrt(theta(r)-t)/sqrt(abs(t-theta(r)))J1-.5(ka(r)+kb(r)+kc(r))*(1-cos(t))*sqrt(theta(r)-t)/sqrt(abs(t-theta(r)))(x,y) = (.5(ka(r)+kb(r)+kc(r))*(t-sin(t))*sqrt(theta(r)-t)/sqrt(abs(t-theta(r))),1-.5(ka(r)+kb(r)+kc(r))*(1-cos(t))*sqrt(theta(r)-t)/sqrt(abs(t-theta(r)))); 0.000000 <= t <= 6.283185OO2??@8?????????8?Нѝҝӝԝ՝֝Pb6r0pi/4(x,y) = (r,0)22 2??@Ke!@@Ke!@???????@Ke!@? cHĀܻ 2sqrt(x)-1+y = 2sqrt(x)-1; 4.000000 <= x <= 25.132741QQ2??@???????ם؝ٝڝ۝ܝݝ`̥$Hnֲ010-(r/4-1)*hvs(r-4)+0*hvs(4-r).seg (0,1) to (0,-(r/4-1)*hvs(r-4)+0*hvs(4-r))QQ2??@?????????? $(,048ƪe01pi/4(x,y) = (0,1)QQ2??@????????ޝߝ\0-(r/4-1)*hvs(r-4)+0*hvs(4-r)pi/4)(x,y) = (0,-(r/4-1)*hvs(r-4)+0*hvs(4-r))QQ2??@8?????????8?<@DHLPT|r-(r/4-1)*hvs(r-4)+0*hvs(4-r)pi/4)(x,y) = (r,-(r/4-1)*hvs(r-4)+0*hvs(4-r))QQ2??@8???????|߫t SS0-(r/4-1)*hvs(r-4)+0*hvs(4-r)r-(r/4-1)*hvs(r-4)+0*hvs(4-r)Iseg (0,-(r/4-1)*hvs(r-4)+0*hvs(4-r)) to (r,-(r/4-1)*hvs(r-4)+0*hvs(4-r))QQ2??@8?????????8?X\`dhlpĵr0pi/4(x,y) = (r,0)QQ2??@8?8??????? X8nݸ\xr-(r/4-1)*hvs(r-4)+0*hvs(4-r)r0.seg (r,-(r/4-1)*hvs(r-4)+0*hvs(4-r)) to (r,0)QQxyzJXT@8?@@@@@@@@@@@@@@@@@@h!@@@@@@@@@n Ln Ln LPI+X-PI/8*X^2+(PI^2/32-1/6)X^3+(PI/12-5PI^3/512)*X^4TTWOp(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٭TTWOClTTWO(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)TTHREEh(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 <= 6KASfWrd1+X^2/4-PI*X^3/16+.1510990443X^4-.1137821991X^5KBA.08402736939X^6-.06102302726X^7+.04369367357X^88@KBB -.03091563799X^9+.02165728736X^10KBC`(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)KCa/La Max IuYA!QpMHM>@R{@*}ATimes New RomanHub  k as a function of r = a/Lr = a/L 朗l<@wjq[@<ݢ?be԰|@Times New RomanHub Minimizing Cycloidr = a/L04.(r/4-1)*hvs(BD?C@?XTtg㾫Times New RomanHub  sqMinimizing "L" Trajectorys(4-r)) to (r,0)/4-1)*hvs(r-4)+0*hTߏ@Q[.@*ǽ9]噰Times New RomanHub  83 (x,y) = (.5(ka(r)+kb(r)+kc(r))*(t-sin(t))*sqrt(theta(r)-t)/s$1b@s*g@n\@B6 u(x,y) = (r,0)$h!@|\XA@y = 2sqrt(x)-1; 4.000000 <= x <= 25.132741$h!@H ?`seg (0,1) to (0,-(r/4-1)*hvs(r-4)+0*hvs(4-r))-1)*hvs(r-4)+0$h!@zbfz(x,y) = (0,1)t(r-4)/sqrt(abs(r-4)),1*sqrt(r-4)/sqrt(abs(r-4$h!@zG(x,y) = (0,-(r/4-1)*hvs(r-4)+0*hvs(4-r))-1)*sqrt(r-4)/sqrt($h!@*GcA]P ! Xw(x,y) = (r,-(r/4-1)*hvs(r-4)+0*hvs(4-r))-1)*sqrt(r-4)/sqrt($h!@zG@seg (0,-(r/4-1)*hvs(r-4)+0*hvs(4-r)) to (r,-(r/4-1)*hvs(r-4)$h!@*GcA(x,y) = (r,0)t(r-4)/sqrt(abs(r-4)),0*sqrt(r-4)/sqrt(abs(r-4$h!@zG seg (r,-(r/4-1)*hvs(r-4)+0*hvs(4-r)) to (r,0)r-4)/sqrt(abs($h!@*GcA