Re: 2 coupled diff. eqns
- To: mathgroup at smc.vnet.net
- Subject: [mg21175] Re: 2 coupled diff. eqns
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 17 Dec 1999 01:22:59 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <831vap$g58@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Henk,
the system appears to be not solvable. You can try it in polar
coordinates with
deqn = {D[f[t], t] == a - (w f[t])/(Sqrt[f[t]^2 + g[t]^2]),
D[g[t], t] == b - (w g[t])/(Sqrt[f[t]^2 + g[t]^2])}
deqn1 = FullSimplify[
Solve[Simplify[
deqn /. Flatten[{#, D[#, t]} & /@ {f[t] -> r[t]*Sin[phi[t]],
g[t] -> r[t]*Cos[phi[t]]}],
Element[r[t], Reals] && r[t] >= 0], {r'[t], phi'[t]}]]
and
DSolve[Flatten[deqn1 /. Rule -> Equal] , {r[t], phi[t]}, t]
But the best seems to make some assuptions on r[t] and phi[t] to get
some limit cases.
Hope that helps
Jens
Henk Jansen wrote:
>
> I have the following set of two coupled differential equations:
>
> c f
> f' = a - ----------------
> ___________
> \ / 2 2
> \/ f + g
>
> c g
> g' = b - ----------------
> ___________
> \ / 2 2
> \/ f + g
>
> where a, b and c are constants. Trying to solve this system (if
> possible), after typing
>
> DSolve[
> {D[f[t], t] == a - (w f[t])/(Sqrt[f[t]^2 + g[t]^2])\),
> D[g[t], t] == b - (w g[t])/(Sqrt[f[t]^2 + g[t]^2])\)
> },
> {f[t], g[t]},
> t]
>
> Mathematica returns with the following message:
>
> "Part::partw: Part 2 of g'[f] does not exist."
>
> without solution. I have two questions:
>
> 1. Does anyone know how to interprete this message?
>
> 2. If the system is not solvable, is there a clever coordinate
> transformation for which the system can be solved?
>
> Thanks,
>
> Henk Jansen