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Some characterizations of gravitational waves emitted from the 2.5 post-Newtonian order Lagrangian dynamics of spinning compact binaries including the next-order spin-orbit contribution and the radiative reaction are detailed. The relationship between the regular and chaotic dynamics and the gravitational waveforms is also described. When the radiative reaction term does not appear in the equations of motion, the gravitational waves are periodic/quasi-periodic for an order conservative binary system, but they seem to be typically irregular for a chaotic one. On the other hand, the binary systems become dissipative and should coalesce if the radiative reaction term is added to the equations of motion. In the dissipative case, the original ordered conservative system can still give regular gravitational waveforms in such a long time before the occurrence of the merging orbits. However, the coalescence time of the binary system corresponding to its original chaotic conservative system is too short to obtain enough information about the characterization of the gravitational waveforms.
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[1] Kidder L E 1995 Phys. Rev. D 52 821
[2] Will C M, Wiseman A G 1996 Phys. Rev. D 54 4813
[3] Gopakumar A, Iyer B R 2002 Phys. Rev. D 65 084011
[4] Blanchet L, Faye G, Iyer B R, Sinha S 2008 Class. Quant. Grav. 25 165003
[5] Tagoshi H, Ohashi A, Owen B J 2001 Phys. Rev. D 63 044006
[6] Faye G, Blanchet L, Buonanno A 2006 Phys. Rev. D 74 104033
[7] Blanchet L, Buonanno A, Faye G 2006 Phys. Rev. D 74 104034
[8] Buonanno A, Chen Y, Damour T 2006 Phys. Rev. D 74 104005
[9] Hergt S, Schafer G 2008 Phys. Rev. D 78 101503
[10] Kokubun F 1998 Phys. Rev. D 57 2610
[11] Suzuki S, Maeda K I 1999 Phys. Rev. D 61 024005
[12] Kiuchi K, Maeda K I 2004 Phys. Rev. D 70 064036
[13] Kiuchi K, Koyama H, Maeda K I 2007 Phys. Rev. D 76 024018
[14] Wang Y, Wu X 2011 Commun. Theor. Phys. 56 1045
[15] Zhong S Y, Liu S 2012 Acta Phys. Sin. 61 120401 (in Chinese) [钟双英, 刘崧 2012 物理学报 61 120401]
[16] Levin J 2000 Phys. Rev. Lett. 84 3515
[17] Schnittman J D, Rasio F A 2001 Phys. Rev. Lett. 87 121101
[18] Cornish N J, Levin J 2002 Phys. Rev. Lett. 89 179001
[19] Konigsdorffer C, Gopakumar A 2005 Phys. Rev. D 71 024039
[20] Hartl M D, Buonanno A 2005 Phys. Rev. D 71 024027
[21] Levin J 2006 Phys. Rev. D 74 124027
[22] Wu X, Xie Y 2007 Phys. Rev. D 76 124004
[23] Wu X, Xie Y 2008 Phys. Rev. D 77 103012
[24] Wu X, Xie Y 2010 Phys. Rev. D 81 084045
[25] Zhong S Y, Wu X 2010 Phys. Rev. D 81 104037
[26] Zhong S Y, Wu X 2011 Acta Phys. Sin. 60 090402 (in Chinese) [钟双英, 伍歆 2011 物理学报 60 090402]
[27] Chen J H, Wang Y J 2003 Chin. Phys. 12 836
[28] Chen J H, Wang Y J 2004 Chin. Phys. 13 583
[29] Chen J H, Wang Y J 2005 Chin. Phys. 14 1282
[30] Chen J H, Wang Y J 2006 Chin. Phys. 15 1705
[31] Wang Y, Wu X 2012 Chin. Phys. B 21 050504
[32] Galaviz P, Brugmann 2011 Phys. Rev. D 83 084013
[33] Wang Y, Wu X 2011 Class. Quantum Grav. 28 025010
[34] Wu X, Zhong S Y 2011Gen. Relat. Gravit. 43 2185
[35] Wu X, Huang T Y 2003 Phys. Lett. A 313 77
[36] Froeschle C, Lega E, Gonczi R 1997 Celest. Mech. Dyn. Astron. 67 41
[37] Wu X, Huang T Y, Zhang H 2006 Phys. Rev. D 74 083001
[38] Li R, Wu X 2010 Acta Phys. Sin. 59 7135 (in Chinese) [李荣, 伍歆 2010 物理学报 59 7135]
[39] Li R, Wu X 2011 Eur. Phys. J. Plus 126 73
[40] Di G H, Xu Y, Xu W, Gu R C 2011 Acta Phys. Sin. 60 020504 (in Chinese) [狄根虎, 许勇, 徐伟, 顾仁财 2011 物理学报 60 020504]
[41] Sun K H, Liu X, Zhu C X 2010 Chin. Phys. B 19 110510
[42] Baker J G, van Meter J R, McWilliams S T, Centrella J, Kelly B J 2007 Phys. Rev. Lett. 99 181101
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