Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy {and} angular momentum. Doubling the phase-space variables of positions and momenta in the coherent equations, we establish extended phase-space symplectic-like integrators with the midpoint permutations. The velocities should be solved iteratively from the algebraic equations of the momenta defined by the Lagrangian during the course of numerical integrations. It is shown numerically that a fourth-order extended phase-space symplectic-like method exhibits good long-term stable error behavior in energy {and} angular momentum, as a fourth-order implicit symplectic method with a symmetric composition of three second-order implicit midpoint rules or a fourth-order Gauss-Runge-Kutta implicit symplectic scheme does. For given time step and integration time, the former method is superior to the latter integrators in computational efficiency. {The extended phase-space method is used to study the effects of the parameters and initial conditions on the orbital dynamics of the coherent Euler-Lagrange equations for a post-Newtonian circular restricted three-body problem. It is also applied to trace the effects of the initial spin angles, initial separation and initial orbital eccentricity on the dynamics of the coherent post-Newtonian Euler-Lagrange equations of spinning compact binaries.
Efficient high-order explicit symplectic splitting methods for post-Newtonian Hamiltonian systems
School of Mathematics, Yunnan Normal University（云南师范大学数学学院）；Yunnan Key Laboratory of Modern Analytical Mathematics and Applications, Yunnan Normal University（云南师范大学现代分析数学及应用云南省重点实验室）
Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem
在早期出版物[Yamada，Asada，Phys. Rev. D 82，104019（2010），83，024040（2011）]中开始的继续工作，我们研究了后牛顿对三体问题拉格朗日等边三角形解的影响。对于三个有限质量，发现等边三角形位形满足广义相对论中后牛顿运动方程，当且仅当三个质量相等.当包含一个测试质量时，等边构型可能有两种情况：（1）一个质量是有限的，另外两个质量是零，或者（2）两个质量是有限且相等的，第三个质量是零，即具有测试质量的对称双星。在质量和边长相同的条件下，后牛顿等边三角形构型的角速度总是小于牛顿构型。
Triangular solution to general relativistic three-body problem for general masses
在早期出版物[Ichita，Yamada和Asada，Phys. Rev. D 83，084026（2011）]中开始的继续工作，我们重新研究了后牛顿对三体问题拉格朗日等边三角形解的影响。对于三个有限质量的三角形位形，当且仅当它的每一个边长都有相对论修正时，它满足广义相对论中的后牛顿运动方程.这个后牛顿配置为三个有限的质量并不总是等边的，它恢复了以前的结果限制三体问题时，一个质量为零。对于相同的质量和角速度，后牛顿三角形构型总是小于牛顿三角形构型。
Observable signature of magnetic tidal coupling in hierarchical triple systems
Università di Perugia（佩鲁贾大学）；I.N.F.N. Sezione di Perugia（意大利国家核物理研究所佩鲁贾分部）；Niels Bohr Institute, Copenhagen University（哥本哈根大学尼尔斯·玻尔研究所）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院与斯德哥尔摩大学）
