哈密顿理论是理论力学和天体力学重要的教学内容.正则坐标和正则坐标变换是哈密顿理论中关键的概念和求解动力学方程的重要技术手段.N体问题描述N个物体或者说天体在彼此万有引力作用下运动的行为.N体问题是理论力学和天体力学课程中教学的重点和难点之一.除十个经典守恒量外，雅可比坐标是N体问题另一个重要的分析手段和方法.通常的教科书只会讲到雅可比坐标的物理含义.本文给出具体的雅可比坐标和惯性坐标的相互变换关系，再使用正则坐标变换的方法给出雅可比坐标对应的共轭动量.这个结果不仅从内容上补全了雅可比坐标关于正则坐标的知识点，同时还给出了正则坐标变换很好的实用范例.文中通过雅可比坐标共轭动量的两种不同推算方法指明了正则坐标变换的技巧关键点.这些内容可以作为理论力学和天体力学课堂教学的有益补充.

Hamiltonian theory is an important teaching content of theoretical mechanics and celestial mechanics. Canonical coordinates and canonical coordinate transformations are key concepts in Hamiltonian theory and important technical means for solving dynamic equations. The N body problem describes the behavior of N objects or celestial bodies moving under the gravitational interaction. The N body problem is one of the key and difficult points in the teaching of theoretical mechanics and celestial mechanics. In addition to ten classical conserved quantities, Jacobi coordinates are another important means and method for the N body problem. Ordinary textbooks only talk about the physical meaning of Jacobi coordinates. In this paper, the specific transformation relationship between Jacobi coordinates and inertial coordinates is given, and then the conjugate momentum corresponding to Jacobi coordinates is given by using the method of canonical coordinate transformation. This result not only complements the knowledge of Jacobi coordinates about canonical coordinates, but also gives a good practical example of canonical coordinate transformation. In this paper, the trick of canonical coordinate transformation are pointed out through two different methods of calculating conjugate momentum of Jacobi coordinates. These contents can be a useful supplement to the classroom teaching of theoretical mechanics and celestial mechanics.