MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Indefinite integration problem on ArcTanh(f(Cos))

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];


f2= Integrate[f1,t];




> 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



  • Prev by Date: Re: Performance comparison Mac OSX vs. Windows XP
  • Next by Date: Re: Indefinite integration problem on ArcTanh(f(Cos))
  • Previous by thread: Indefinite integration problem on ArcTanh(f(Cos))
  • Next by thread: Re: Indefinite integration problem on ArcTanh(f(Cos))