We investigate the orbits of compact binary systems during the final inspiral period before coalescence by integrating numerically the second-order post-Newtonian equations of motion .
We include spin-orbit and spin-spin coupling terms , which , according to a recent study by Levin [ J. Levin , Phys .
Rev .
Lett . 84 , 3515 ( 2000 ) ] , may cause the orbits to become chaotic .
To examine this claim , we study the divergence of initially nearby phase-space trajectories and attempt to measure the Lyapunov exponent \gamma .
Even for systems with maximally spinning objects and large spin-orbit misalignment angles , we find no chaotic behavior .
For all the systems we consider , we can place a strict lower limit on the divergence time t _ { L } \equiv 1 / \gamma that is many times greater than the typical inspiral time , suggesting that chaos should not adversely affect the detection of inspiral events by upcoming gravitational-wave detectors .