       • To: mathgroup at smc.vnet.net
• Subject: [mg90920] Re: Adding assumptions to SOLVE
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Tue, 29 Jul 2008 06:10:38 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g6mauf\$i27\$1@smc.vnet.net>

```Joe Hays wrote:

> Newbie question.
>
> SOLVE documentation indicates I have to include assumptions to solve this (I
> thought) simple problem:
>
> <snip>
> r[t] = {x[t] - L*Sin[q[t]], L*Cos[q[t]]};
> r'[t] = D[r[t], t];
> r''[t] = D[r'[t], t];
>
> Eq1 =  Mc*x''[t] - u + N
> Eq2 = Mp*({1, 0}.r''[t]) - N
> Eq3 =  Mp*({0, 1}.r''[t]) - P + Mp*g
> Eq4 = J*q''[t] - P*L*Sin[q[t]] - N*L*Cos[q[t]]
>
> Solve[{Eq1 == 0, Eq2 == 0, Eq3 == 0, Eq4 == 0}, {x''[t], q''[t]}]
> </snip>
>
> My assumptions are:
>
>    - N > 0
>    - P > 0
>    - g > 0
>    - L > 0
>    - Mc > 0
>    - Mp > 0
>
> Yet, I can't figure out how to get Solve to return the sybolic equations for
> x''[t] and q''[t]. What am I missing?

I am dubitative by what you wrote, since:

Solve[] mostly solve linear and polynomial equations and
*cannot* handle inequalities.

Reduce[] does handle inequalities as well as a larger range of
functions than Solve[].

Neither Solve[] nor Reduce[] will solve differential equations.

However, *DSolve[]* is designed to solve differential equations.

Therefore, you should use DSolve[] to solve for x and q of t, then you
can get their second derivative w.r.t t.

HTH,
-- Jean-Marc

```

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