Solving Intractable Integral: \frac{1}{(1+a cos(\theta - \phi))^2}

[ice109]

What is the usual course of action if there isn't an analytical inverse?

depends on what you want to use the inverse for?

Ignore the problem and move on.
Its not like this is part of a Masters Thesis Research...

what range for theta?

 

[NoobixCube]

say from 0 4pi , or any range that might show the functions periodicy

 

[n0_3sc]

Now that I look at your problem - It definitely reminds me of "Elliptical Integrals".
Wiki it and I'm sure you'll find something useful.

 

[ice109]

take this as a hint; get mathematica

 

[n0_3sc]

What is the usual course of action if there isn't an analytical inverse?

Apparently its "Get Mathematica".

 

[Gib Z]

If you mean elementary anti derivative, then a) If you have limits of integration, numerical methods, or b) Define it as a new function ! =]

 

[NoobixCube]

Thanks for taking the time ice109

 

[coomast]

You can solve this integral by considering it after the simple substitution:

\theta- \phi=t

as:

\int\frac{dt}{(1+acos(t))^2}

Now use the substitution:

1+acos(t)=\frac{1-a^2}{1-acos(t)}

You will easily arrive at the solution.

Take a look at an older post of me where I explain this substitution a bit more:

https://www.physicsforums.com/showthread.php?t=204639

Hope this helps.