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Re: Indefinite integration problem on ArcTanh(f(Cos))
*To*: mathgroup at smc.vnet.net
*Subject*: [mg69944] Re: Indefinite integration problem on ArcTanh(f(Cos))
*From*: dh <dh at metrohm.ch>
*Date*: Thu, 28 Sep 2006 06:14:40 -0400 (EDT)
*References*: <efdks2$12a$1@smc.vnet.net>
Hi Andrew,
your integral contains multivalued functions like PolyLog and Log and I
suspect that you are having a branch cut problem. However, if you do not
need an analytic result, it is much easier to do this numerically. E.g.
setting k=0.8:
f0=Interpolation[ Table[{t,Sin[t]/(1+0.8 Cos[2t])},{t,0,10,.1}] ];
f1= Integrate[Evaluate[f0[t]],t];
Plot[f1,{t,0,10}]
f2= Integrate[f1,t];
Plot[f2,{t,0,10}]
Daniel
ANDREW PALFREYMAN wrote:
> Hi.
> I'm integrating Sin[t] / (1 + k Cos[2t]) , over 0 < k < 1, using Mathematica 4.1. I'm plotting spot values k=0.1, 0.8, 0.95 over 0
> < t < 10.
>
> This represents the acceleration of a charged particle in an alternating electric field, where k represents a particular modulation
> of its effective inertia. Although the velocity plots (the integral dt) look fine (symmetrical about zero), the plots for position
> (integrating velocity dt) are clearly wrong; I get a massive expression (about 20 lines!) which will not differentiate successfully
> back to the original velocity expression, and they are decidedly asymmetrical about zero. The position plot ought to look like a
> sinewave as k->0, but there's no resemblance.
>
> Andrew Palfreyman
>
>
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