Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are discussed within the most often applied Arnowitt–Deser–Misner formalism. The obtention of autonomous Hamiltonians is achieved by the transition to Routhians. Order reduction of higher derivative Hamiltonians results in standard Hamiltonians. Tetrad representation of general relativity is introduced for the tackling of compact binaries with spinning components. Configurations are treated where the absolute values of the spin vectors can be considered constant. Compact objects are modeled by use of Dirac delta functions and their derivatives. Consistency is achieved through transition to d-dimensional space and application of dimensional regularization. At the fourth post-Newtonian level, tail contributions to the binding energy show up. The conservative spin-dependent dynamics finds explicit presentation in Hamiltonian form through next-to-next-to-leading-order spin–orbit and spin1–spin2 couplings and to leading-order in the cubic and quartic in spin interactions. The radiation reaction dynamics is presented explicitly through the third-and-half post-Newtonian order for spinless objects, and, for spinning bodies, to leading-order in the spin–orbit and spin1–spin2 couplings. The most important historical issues get pointed out.

哈密​​顿形式主义为计算爱因斯坦场方程的近似解析解提供了强大的工具。紧致双星的显式解析动力学和运动的后牛顿计算在最常应用的阿诺维特-德瑟-米斯纳形式主义中进行了讨论。自主哈密顿主义者的获得是通过向劳斯主义者的过渡而实现的。高阶导数哈密顿量的降阶会产生标准哈密顿量。引入广义相对论的四分体表示来解决具有旋转组件的致密双星。处理配置时，自旋向量的绝对值可以被认为是恒定的。紧凑物体是通过使用狄拉克δ函数及其导数来建模的。一致性是通过过渡到d维空间并应用维数正则化来实现的。在第四后牛顿能级，结合能的尾部贡献显现出来。保守的自旋相关动力学通过次次次前导自旋轨道和自旋 1-自旋 2 耦合以及自旋相互作用中三次和四次的前导顺序以哈密顿形式明确表示。对于无自旋物体，辐射反应动力学通过三分半后牛顿阶明确地表示，而对于旋转体，则通过自旋轨道和自旋 1 - 自旋 2 耦合中的前导阶来表示。指出了最重要的历史问题。