- #1
thrillhouse86
- 80
- 0
Hi all,
I am trying to determine two Melnikov Integrals (after some manipulation) of the form:
[tex]\int^{\infty}_{-\infty}cos(at)sech(bt) dt[/tex]
and
[tex]\int^{\infty}_{-\infty}cos(at)sech^{3}(bt) dt[/tex]
The textbook I've been reading (Litchenberg & Libermann), says that the way to integrate similar problems is to use the method of residues. I have a superficial understanding of how that works, but every other time I've used the method of residue I've dealt with rationale functions so that I could find poles and then just apply apply the Cauchy integral formula at the isolated poles.
Can anyone give me a kick-start on how to begin solving these 2 integrals by the method of residues ?
I am trying to determine two Melnikov Integrals (after some manipulation) of the form:
[tex]\int^{\infty}_{-\infty}cos(at)sech(bt) dt[/tex]
and
[tex]\int^{\infty}_{-\infty}cos(at)sech^{3}(bt) dt[/tex]
The textbook I've been reading (Litchenberg & Libermann), says that the way to integrate similar problems is to use the method of residues. I have a superficial understanding of how that works, but every other time I've used the method of residue I've dealt with rationale functions so that I could find poles and then just apply apply the Cauchy integral formula at the isolated poles.
Can anyone give me a kick-start on how to begin solving these 2 integrals by the method of residues ?