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Re: problems with NDSolve

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  • Subject: [mg131151] Re: problems with NDSolve
  • From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
  • Date: Fri, 14 Jun 2013 05:02:55 -0400 (EDT)
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i,

I'm new in Mathematica and have a problem you can maybe help me with. I try to solve the differential equation given by T. G. Myers and J. P. F. Charpin (http://dx.doi.org/10.1063/1.3155185) as follows:

rho  = 1700
g = 9.81
sigma = 0.00001
c = rho g / sigma
z0 = 0.1
sol = NDSolve[{x'[t] ==
    c (z0 - z[t]) - tan[x[t]]/(r Sqrt[1 + tan[x[t]]^2]) ,
   y'[t] == cos[x[t]], z'[t] == sin[x[t]], x[0] == 0.0001, y[0] == 0,
   z[0] == 0}, {x[t], y[t], z[t]} , {t, 0, 1} ]

I get this result and don't know what to do.

Hi, Axel,

Your code is almost correct. There are two small things: (1) Write Tan, Sin and Cos instead of tan, sin and cos and (2) fix the numeric value of parameter r. Then it works. Try this:

rho = 17
g = 9.81
sigma = 0.00001
c = rho g/sigma
z0 = 0.1
r = 1;
sol = NDSolve[{x'[t] ==
    c (z0 - z[t]) - Tan[x[t]]/(r Sqrt[1 + Tan[x[t]]^2]),
   y'[t] == Cos[x[t]], z'[t] == Sin[x[t]], x[0] == 0.0001, y[0]== 0,
   z[0] == 0}, {x[t], y[t], z[t]}, {t, 0, 1}]

and then evaluate this:

ParametricPlot3D[Evaluate[{x[t], y[t], z[t]} /. sol], {t, 0, 1}]

Note that I changed the values of some parameters. With your original values one can see nothing on the graphics.

Have fun, Alexei

Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
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Office phone :  +352-2454-2566
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e-mail: alexei.boulbitch at iee.lu






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