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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
the right answer.):

{
 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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