Third order ODE not working

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• Subject: [mg131719] Third order ODE not working
• From: Narasimham <mathma18 at gmail.com>
• Date: Mon, 23 Sep 2013 21:59:30 -0400 (EDT)
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```<<Calculus `VectorAnalysis `

(* Attempting to find zero torsion and constant angle of plane section lines and meridian on a surface of revolution. Torsion formula is standard and verified, second equation in ode is for cotangent of required angle *)

X[u_]={ R[u] Cos[u],R[u] Sin[u], Z[u] }
Tau[t_]=FullSimplify[ ScalarTripleProduct[ X'[t],X''[t],X'''[t] ]  ]
Tau[t_]=3 Z[t] (R^)[t]2-R[t] (3 R[t] Z[t]+2 Z[t] R(3)[t])+R[t]2 (Z[t]+Z(3)[t])+2 (R^)[t]2 (3 Z[t]+Z(3)[t])-R[t] (Z[t] (2 R[t]-R(3)[t])+R[t] (4 Z[t]+Z(3)[t])) ;

cotal=Sqrt[3.] ;

NDSolve[  {Tau[t]== 0. ,Sqrt[Z'[t]^2+R'[t]^2]R[t] cotal, Z''[0]==0.05,Z'[0]==5.0,Z[0]==4., R''[0]==0.2,R'[0]==-.04, R[0]==3.},{R,Z}, {t,0,5.} ]

{Primes print as small squares here, carat for exponent missing)