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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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