ω_{1} = \frac{∂^{2}}{∂t^{2}} (ξ(t) − \frac{ϵ \frac{d^{2}}{dt^{2}} ξ(t)}{\sqrt{(\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2}}} )  (1)

ω_{2} = \frac{∂^{2}}{∂t^{2}} (ζ(t) − \frac{ϵ (\frac{d^{2}}{dt^{2}} ζ(t) + 1)}{\sqrt{(\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2}}} )  (2)

ω_{1} = \frac{d^{2}}{dt^{2}} ξ(t) − \frac{ϵ \frac{d^{4}}{dt^{4}} ξ(t)}{\sqrt{(\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2}}} + \frac{ϵ (\frac{d^{3}}{dt^{3}} ξ(t)) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} −

− 3/4 \frac{ϵ (\frac{d^{2}}{dt^{2}} ξ(t)) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))^{2}}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{5/2}} +

+ 1/2 \frac{ϵ (\frac{d^{2}}{dt^{2}} ξ(t)) (2 (\frac{d^{3}}{dt^{3}} ξ(t))^{2} + 2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{4}}{dt^{4}} ξ(t) + 2 (\frac{d^{3}}{dt^{3}} ζ(t))^{2} + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{4}}{dt^{4}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}}  (3)

ω_{2} = \frac{d^{2}}{dt^{2}} ζ(t) − \frac{ϵ \frac{d^{4}}{dt^{4}} ζ(t)}{\sqrt{(\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2}}} + \frac{ϵ (\frac{d^{3}}{dt^{3}} ζ(t)) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} −

− 3/4 \frac{ϵ (\frac{d^{2}}{dt^{2}} ζ(t) + 1) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))^{2}}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{5/2}} +

+ 1/2 \frac{ϵ (\frac{d^{2}}{dt^{2}} ζ(t) + 1) (2 (\frac{d^{3}}{dt^{3}} ξ(t))^{2} + 2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{4}}{dt^{4}} ξ(t) + 2 (\frac{d^{3}}{dt^{3}} ζ(t))^{2} + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{4}}{dt^{4}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} (4)

\frac{d^{4}}{dt^{4}} ξ(t)\frac{ϵ (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2}}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} = ω_{1} − \frac{d^{2}}{dt^{2}} ξ(t) − \frac{ϵ (\frac{d^{3}}{dt^{3}} ξ(t)) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} +

+ 3/4 \frac{ϵ (\frac{d^{2}}{dt^{2}} ξ(t)) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))^{2}}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{5/2}} −

− 1/2 \frac{ϵ (\frac{d^{2}}{dt^{2}} ξ(t)) (2 (\frac{d^{3}}{dt^{3}} ξ(t))^{2} + 2 (\frac{d^{3}}{dt^{3}} ζ(t))^{2} + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{4}}{dt^{4}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} (5)

\frac{d^{4}}{dt^{4}} ξ(t)\frac{ϵ (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2}}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} = \frac{1}{(\frac{d^{2}}{dt^{2}} ξ(t))} [ω_{2} − \frac{d^{2}}{dt^{2}} ζ(t) + \frac{ϵ \frac{d^{4}}{dt^{4}} ζ(t)}{\sqrt{(\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2}}} −

− \frac{ϵ (\frac{d^{3}}{dt^{3}} ζ(t)) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} +

+ 3/4 \frac{ϵ (\frac{d^{2}}{dt^{2}} ζ(t) + 1) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))^{2}}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{5/2}} −

− \frac{ϵ (\frac{d^{2}}{dt^{2}} ζ(t) + 1) ( (\frac{d^{3}}{dt^{3}} ξ(t))^{2} + (\frac{d^{3}}{dt^{3}} ζ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{4}}{dt^{4}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} ] (6)

\frac{d^{4}}{dt^{4}} ξ(t)\frac{ϵ (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2}}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} = ω_{1} − \frac{d^{2}}{dt^{2}} ξ(t) − \frac{ϵ (\frac{d^{3}}{dt^{3}} ξ(t)) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} +

+ 3/4 \frac{ϵ (\frac{d^{2}}{dt^{2}} ξ(t)) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))^{2}}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{5/2}} −

− 1/2 \frac{ϵ (\frac{d^{2}}{dt^{2}} ξ(t)) (2 (\frac{d^{3}}{dt^{3}} ξ(t))^{2} + 2 (\frac{d^{3}}{dt^{3}} ζ(t))^{2} + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{4}}{dt^{4}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} (7)

\frac{d^{4}}{dt^{4}} ζ(t) \frac{−ϵ \frac{d^{2}}{dt^{2}} ξ(t)}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} = ω_{2} − \frac{d^{2}}{dt^{2}} ζ(t) − \frac{ϵ (\frac{d^{3}}{dt^{3}} ζ(t)) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}} +

+ 3/4 \frac{ϵ (\frac{d^{2}}{dt^{2}} ζ(t) + 1) (2 (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{3}}{dt^{3}} ξ(t) + 2 (\frac{d^{2}}{dt^{2}} ζ(t) + 1) \frac{d^{3}}{dt^{3}} ζ(t))^{2}}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{5/2}} −

− \frac{ϵ (\frac{d^{2}}{dt^{2}} ζ(t) + 1) ( (\frac{d^{3}}{dt^{3}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ξ(t)) \frac{d^{4}}{dt^{4}} ξ(t) + (\frac{d^{3}}{dt^{3}} ζ(t))^{2})}{((\frac{d^{2}}{dt^{2}} ξ(t))^{2} + (\frac{d^{2}}{dt^{2}} ζ(t) + 1)^{2})^{3/2}}  (8)

ξ(t) = r_{1} (\frac{t − T_{1}}{t_{2} − T_{1}} )^{5} − r_{2} (\frac{t − T_{1}}{t_{2} − T_{1}} )^{6} + r_{3} (\frac{t − T_{1}}{t_{2} − T_{1}} )^{7} − r_{4} (\frac{t − T_{1}}{t_{2} − T_{1}} )^{8} + r_{5} (\frac{t − T_{1}}{t_{2} − T_{1}} )^{9} − r_{6} (\frac{t − T_{1}}{t_{2} − T_{1}} )^{10}
ξ(t) = \frac{63}{25000} t^{5} − \frac{21}{20000} t^{6} + \frac{9}{50000} t^{7} − \frac{63}{4000000} t^{8} + \frac{7}{10000000} t^{9} − \frac{63}{5000000000} t^{10}

ζ(t) = \frac{D^{2}}{4} + ϵ − (ξ(t) − \frac{D}{2} )^{2}

ζ(t) = 0.270 − (\frac{63}{25000} t^{5} − \frac{21}{20000} t^{6} + \frac{9}{50000} t^{7} − \frac{63}{4000000} t^{8} + \frac{7}{10000000} t^{9} − \frac{63}{5000000000} t^{10} − 1/2)^{2}

Entrada.  Trayectoria

ξ(t) = −\frac{63}{5000000000} t^{10} + \frac{7}{10000000} t^{9} − \frac{63}{4000000} t^{8} + \frac{9}{50000} t^{7} − \frac{21}{20000} t^{6} + \frac{63}{25000} t^{5}

\frac{d}{dt}ξ(t) = −\frac{63}{500000000} t^{9} + \frac{63}{10000000} t^{8} − \frac{63}{500000} t^{7} + \frac{63}{50000} t^{6} − \frac{63}{10000} t^{5} + \frac{63}{5000} t^{4}

\frac{d^{2}}{dt^{2}} ξ(t) = −\frac{567}{500000000} t^{8} + \frac{63}{1250000} t^{7} − \frac{441}{500000} t^{6} + \frac{189}{25000} t^{5} − \frac{63}{2000} t^{4} + \frac{63}{1250} t^{3}

\frac{d^{3}}{dt^{3}} ξ(t) = −\frac{567}{62500000} t^{7} + \frac{441}{1250000} t^{6} − \frac{1323}{250000} t^{5} + \frac{189}{5000} t^{4} − \frac{63}{500} t^{3} + \frac{189}{1250} t^{2}

\frac{d^{4}}{dt^{4}} ξ(t) = −\frac{3969}{62500000} t^{6} + \frac{1323}{625000} t^{5} − \frac{1323}{50000} t^{4} + \frac{189}{1250} t^{3} − \frac{189}{500} t^{2} + \frac{189}{625} t  (9)

ζ(t) = 0.270 − (−\frac{63}{5E09} t^{10} + \frac{7}{10E06} t^{9} − \frac{63}{4E06} t^{8} + \frac{9}{50E03} t^{7} − \frac{21}{20E03} t^{6} + \frac{63}{25000} t^{5} − 1/2)^{2}

\frac{d}{dt}ζ(t) = −\frac{3969}{1250E15} t^{19} + \frac{8379}{25E15} t^{18} − \frac{79821}{5E15} t^{17} + \frac{225981}{500E12} t^{16} − \frac{210609}{25E12} t^{15} + \frac{1350657}{12500E09} t^{14} − \frac{483021}{500E09} t^{13} + \frac{297297}{50E09} t^{12} −
− \frac{60291}{2500E06} t^{11} + \frac{14553}{250E06} t^{10} − \frac{6363}{100E06} t^{9} + \frac{63}{10E06} t^{8} − \frac{63}{500E03} t^{7} + \frac{63}{50E03} t^{6} − \frac{63}{10E03} t^{5} + \frac{63}{5E03} t^{4}

\frac{d^{2}}{dt^{2}} ζ(t) = −\frac{75411}{1.25E18} t^{18} + \frac{75411}{12.5E15} t^{17} − \frac{1356957}{5E15} t^{16} + \frac{225981}{31.25E12} t^{15} − \frac{631827}{5E12} t^{14} + \frac{9454599}{6.25E12} t^{13} − \frac{6279273}{0.5E12} t^{12} + \frac{891891}{12.5E09} t^{11} −
− \frac{663201}{2.5E09} t^{10} + \frac{14553}{25E06} t^{9} − \frac{57267}{0.1E09} t^{8} + \frac{63}{1250000} t^{7} − \frac{441}{0.5E06} t^{6} + \frac{189}{25E03} t^{5} − \frac{63}{2E03} t^{4} + \frac{63}{1250} t^{3}

\frac{d^{3}}{dt^{3}} ζ(t) = −\frac{678699}{625E15} t^{17} + \frac{1281987}{12.5E15} t^{16} − \frac{1356957}{312.5E12} t^{15} + \frac{677943}{6.25E12} t^{14} − \frac{4422789}{2.5E12} t^{13} + \frac{122909787}{6.25E12} t^{12} − \frac{18837819}{125E09} t^{11} + \frac{9810801}{12.5E09} t^{10} −
− \frac{663201}{250E06} t^{9} + \frac{130977}{25E06} t^{8} − \frac{57267}{12.5E06} t^{7} + \frac{441}{1.25E06} t^{6} − \frac{1323}{250E03} t^{5} + \frac{189}{5E03} t^{4} − \frac{63}{500} t^{3} + \frac{189}{1250} t^{2}

\frac{d^{4}}{dt^{4}} ζ(t) = −\frac{11537883}{625E15} t^{16} + \frac{1281987}{781.25E12} t^{15} − \frac{4070871}{62.5E12} t^{14} + \frac{4745601}{3125E09} t^{13} − \frac{57496257}{2.5E09} t^{12} + \frac{368729361}{1562.5E09} t^{11} − \frac{207216009}{125E09} t^{10} +
+ \frac{9810801}{1.25E09} t^{9} − \frac{5968809}{250E06} t^{8} + \frac{130977}{3.125E06} t^{7} − \frac{400869}{12.5E06} t^{6} + \frac{1323}{625E03} t^{5} − \frac{1323}{50E03} t^{4} + \frac{189}{1250} t^{3} − \frac{189}{500} t^{2} + \frac{189}{625} t  (10)