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MathGroup Archive 1999

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Re: How NDSolve counts Conditions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18800] Re: [mg18782] How NDSolve counts Conditions
  • From: "Richard Finley" <rfinley at medicine.umsmed.edu>
  • Date: Thu, 22 Jul 1999 08:19:22 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Jay,
Try adding the two missing solutions to your solution set: {x[t],vx[t],y[t]
,vy[t]} rather than just the {x[t],y[t]} and I think you will find it 
works OK.    RF

>>> "jay nospam beatty" <nhi at nospam_netaxis.com> 07/19/99 11:33PM >>>
I've been trying to build a simple earth orbit model:

orbitsolution[x0_, vx0_, y0_ , vy0_] :=

NDSolve[ {x'[t] == vx[t],
               vx'[t] == -gravParam /(dis[t]^2) * Cos[\[Phi][t]] ,
               y'[t] == vy[t],
               vy'[t] ==  -gravParam /(dis[t]^2) * Sin[\[Phi][t]]  ,
       x[0] == x0,  vx[0] == vx0, y[0] == y0, vy[0] == vy0 
} ,
          {x[t] , y[t]}  ,  { t,0,10^8}   ]

As far as I can see, I have 4 diff equations and 4 conditions.

Yet when I try for an altitude of 700,000 km and y velocity of 100 km/sec, 
I get:

fullsolorbitsolution[7 10^5,  0 ,  0  ,  100]


NDSolve::"ndnef":
    "The number of differential equations (\!\(4\)) is not equal to the \
number of initial conditions (\!\(2\))."


I get the same result if I reduce my conditions - even to none!

On the other hand it does not have the same problem if I don't define
velocity, but only acceleration:

torbitsolution[x0_, vx0_, y0_ , vy0_] :=
        NDSolve[ {x''[t]
                               == -gravParam /(dis[t]^2) * Cos[\[Phi][t]] ,
                      y''[t]
                                ==  -gravParam /(dis[t]^2) * Sin[\[Phi][t]]
,

                 x[0] == x0,  x'[0] == vx0, y[0] == y0, y'[0] == vy0 } ,
           {x[t] , y[t]}    ,    { t,0,10^8}]


fullsoltorbitsolution[7 10^5,  0 ,  0  ,  100]

which gives me a list of interpolating functions I can't seem to copy.


How is M counting equations and conditions?

Thanks.


Jay








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