Third order ODE not working
- To: mathgroup at smc.vnet.net
- 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)
Not working, please help.( Non-numerical, not all Solve variables can be found etc. error msgs).
Regards
Narasimham