       Reduce with system of equations involving D

• To: mathgroup at smc.vnet.net
• Subject: [mg113824] Reduce with system of equations involving D
• From: Eduardo Cavazos <wayo.cavazos at gmail.com>
• Date: Sun, 14 Nov 2010 06:10:31 -0500 (EST)

```Hello,

Here I'm using Reduce on a system of equations to find 'a'
symbolically:

{
\[CapitalSigma]\[Tau] ==
D[Subscript[m, 1]*v*R + Subscript[m, 2]*v*R + \[CapitalIota]*v/R, t,
NonConstants -> {v}],
\[CapitalSigma]\[Tau] == Subscript[m, 1]*g*R,
a == D[v, t, NonConstants -> v],
Subscript[m, 1] > 0, Subscript[m, 2] > 0, g > 0,
R > 0, \[CapitalIota] > 0
}
Reduce[%, {a, D[v, t, NonConstants -> v], \[CapitalSigma]\[Tau]}]

The answer is correct. However, I had to simplify the set of equations
slightly.

I'd like to say that:

\[CapitalSigma]\[Tau] == D[L[t], t]

where:

L == Subscript[m, 1]*v*R + Subscript[m, 2]*v*R + \[CapitalIota]*v/R

So something like this (Just to give you an idea. This doesn't produce

{
L == Subscript[m, 1]*v*R + Subscript[m, 2]*v*R + \[CapitalIota]*v/R,
\[CapitalSigma]\[Tau] == D[L[t], t],
\[CapitalSigma]\[Tau] == Subscript[m, 1]*g*R,
a == D[v, t, NonConstants -> v],
Subscript[m, 1] > 0, Subscript[m, 2] > 0, g > 0,
R > 0, \[CapitalIota] > 0
}
Reduce[%, {a, D[v, t, NonConstants -> v], \[CapitalSigma]\[Tau]}]

Thanks for any suggestions.

Ed

```

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