The Lagrangian Dynamics Of Post-Newtonian Spinning Compact Binaries

The existence of gravitational wave is one of four predictions from the general relativistic theory proposed by Einstein. With the advance of modern celestial mechanics and astrophysics, the detection of gravitational waves has turned out to be one of the hotspots of scientific research, which need take precisely theoretical template as the foundation. Thus, the dynamics of sources of gravitational waves in the universe are required to have more accurately theoretical analysis. As the most promising sources for gravitational-wave detectors a result, the spinning compact binary system, especially their dynamics, have become an interesting topic in the celestial physical society.In this thesis, based on the studies of fore-men we mainly discussed the dynamics and gravitational waveforms of relativistic spinning compact binary systems as to the comparable-mass using a certain method of numerical integration and chaotic identification.On one hand, the paper is mainly devoted to numerically investigating the effects of the next-order spin-orbit interactions including the 2.5 PN order term of the equations of motion and the 2PN order terms of the spin precession equations on chaos in the conservative Lagrangian dynamics of a spinning compact binary system. It is shown sufficiently through individual orbit simulations, the dependence of the invariant fast Lyapunov indicators on the variations of initial spin angles and the phase space scans for chaos, that the next-order spin-orbit contributions do play an important role in the amplification of chaos.On the other hand, the paper is mainly applied to numerically studying the effects of next-order spin-orbit interactions on gravitational waveforms in the conservative Lagrangian dynamics of a spinning compact binary system, and analyzing the influence of dissipative term on gravitational waveforms in FBB model. Dependence of the method of power spectrum, we find the contribution of next-order spin-orbit interactions do not only make the behavior of chaos stronger but also urge the waveforms to change in terms of the dynamics. In addition, we confirm that the waveforms of the ordered orbits emission are regular and periodic, and ones of the chaotic orbits are irregular and aperiodic again. According to investigation into the case of considering the radiation reaction, we conclude that existence of the term make the gravitational waves radiated from the two kinds of orbits stop in a short time of integration. Through numerical simulation analysis, we find the introduction of the dissipation terms lead to coalescence after a period of evolution of the two bodies of spinning compact binary system.