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 /==================================================\ | Dept. of Mathematics | Internet: lehtonen at jyu.fi | | Univ. of Jyvaskyla | Phone : +358 41 602 718 | | P.O Box 35 | Fax : +358 41 602 701 | | SF-40351 Jyvaskyla, FINLAND | \==================================================/