Chinese Physics, 2005, Vol. 14(4): 660-662    DOI: 10.1088/1009-1963/14/4/004
 GENERAL Prev   Next

# The parametric orbits and the form invariance of three-body in one-dimension

Lou Zhi-Mei (楼智美)
Department of Physics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China
Abstract  In this paper, the differential equations of motion of a three-body interacting pairwise by inverse cubic forces (centrifugal potential'') in addition to linear forces (harmonical potential'') are expressed in Ermakov formalism in two-dimension polar coordinates, and the Ermakov invariant is obtained. By rescaling of the time variable and the space coordinates, the parametric orbits of the three bodies are expressed in terms of relative energy H1 and Ermakov invariant. The form invariance of the transformations of two conserved quantities are also studied.
Keywords:  three-body      parametric orbits      Ermakov invariant      Hamiltonian function      conserved quan-tities      form invariance
Received:  10 October 2004      Revised:  03 November 2004      Accepted manuscript online:
 PACS: 45.50.Jf (Few- and many-body systems ?) 45.05.+x (General theory of classical mechanics of discrete systems) 45.20.Jj (Lagrangian and Hamiltonian mechanics)