Sreenath, N., Y. G. Oh, P. S. Krishnaprasad, and J. E. Marsden
The dynamics on the reduced space for two bodies occurs on cylinders in 3; stability of the equilibria is studied using the energy-Casimir method and is confirmed numerically. The phase space of the two bodies contains a homoclinic orbit which produces chaotic solutions when the system is perturbed by a third body. This and a study of periodic orbits are discussed in part II. The number and stability of equilibria and their bifurcations for three bodies as system parameters are varied are studied here; in particular, it is found that there are always four or six equilibria.