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Elliptic integral problems in mma
*To*: mathgroup at yoda.physics.unc.edu
*Subject*: Elliptic integral problems in mma
*From*: Ari Lehtonen <lehtonen at kalikka.jyu.fi>
*Date*: Mon, 26 Oct 1992 15:27:37 +0200
While preparing notes for my course on ODE, I found a bug
in mma's elliptic integrals (Mathematica 2.0 for SPARC).
JacobiAmplitude should give the solution to the eqution
of the pendulum:
y'' + g/l Sin[y] == 0
initial cond: y[0]==0, y'[0]==z0 > 0
==> y[t] == 2 JacobiAmplitude[ z0 t/2 , 4g/(z0^2 l)]
But the plotted result didn't look very nice.
You can see problems in the following:
In[2]:= m=1.5;
In[3]:= Plot[JacobiAmplitude[x,m],{x,0,7}];
In[4]:= Plot[ArcSin[JacobiSN[x,m]],{x,0,7}];
The above curves should be the same (and are not on my mma).
Similarly the following two curves differ (while they shouldn't):
In[5]:= Plot[{Sin[JacobiAmplitude[x,m]], JacobiSN[x,m]},{x,0,7}];
Note that the parameter m > 1 (periodic solution).
The case m<1 corresponds to a strictly increasing
y=y[t] (initial push z0 large enough), and in this
case there is only one curve in Out[5].
Can anybody point out what is wrong.
Ari Lehtonen
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