关键词: 哈密顿, 正则坐标, 正则坐标变换, 雅可比坐标

Abstract: 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.

Key words:  Hamilton, canonical coordinate, canonical coordinate transformation, Jacobi coordinate