Re: Solve how to eliminate variable

• To: mathgroup at smc.vnet.net
• Subject: [mg105293] Re: [mg105269] Solve how to eliminate variable
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Thu, 26 Nov 2009 06:14:41 -0500 (EST)

```Hi, Peter,
you may get what you want, if point out the variables that you want to exclude in the list of unknown variables in Solve:

eq1 = \[CurlyPhi]''[t] == F[t];
eq2 = F[t] == Fp[t] - Ft[t] - Fv[t];
eq3 = \[CurlyPhi]'[t] == Fp[t]/(l*kp);
eq4 = \[CurlyPhi][t] == Ft[t]/(m*g);

sol = Solve[{eq1, eq2, eq3, eq4}, {\[CurlyPhi]''[t], F[t], Ft[t],
Fp[t]}];
sol[[1, 1]]

\!\(\*SuperscriptBox["\[CurlyPhi]", "\[Prime]\[Prime]",
MultilineFunction->None]\)[t] -> -Fv[t] - g m \[CurlyPhi][t] + kp l
\!\(\*SuperscriptBox["\[CurlyPhi]", "\[Prime]",
MultilineFunction->None]\)[t]

Have success, Alexei

Hi dears,
I am using Solve to get differential equation from set of linear  and
differential equation. When I use code like this

Solve[{
Subscript[F, t] == g m \[Phi][t],
l Subscript[k, p]
\!\(\*SuperscriptBox["\[Phi]", "\[Prime]",
MultilineFunction->None]\)[t] == Subscript[F, p],
l m
\!\(\*SuperscriptBox["\[Phi]", "\[Prime]\[Prime]",
MultilineFunction->None]\)[t] == F,
-F == -Subscript[F, p] + Subscript[F, t] + Subscript[F, v],
}, \[Phi]''[t]]

I obtain result like

{{
\!\(\*SuperscriptBox["\[Phi]", "\[Prime]\[Prime]",
MultilineFunction->None]\)[t] -> F/(l m)}}

but my goal is get result containing Fv:

{{
\!\(\*SuperscriptBox["\[Phi]", "\[Prime]\[Prime]",
MultilineFunction->None]\)[t] -> (-Subscript[F, v] - g m \[Phi][t] +
l Subscript[k, p]
\!\(\*SuperscriptBox["\[Phi]", "\[Prime]",
MultilineFunction->None]\)[t])/(l m)}}

Can somebody help me how to do this using Solve or witch function to
use. I wouldn't like to use Rule and Replace.

Thanks
Petr Martinec

--
Alexei Boulbitch, Dr., habil.
Senior Scientist

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```

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