Resonant periodic orbits in the problem of three bodies
Abstract
The evolution of families of resonant periodic orbits in the circular and elliptic restricted problem into families of the general problem is studied. A systematic approach is introduced to generate resonant periodic orbits in the circular, elliptic restricted and the general threebody problem. The bifurcation phenomena in the restricted problem are studied, analyzed and compared with the bifurcation phenomena in the general problem. A new method to determine the linear stability of periodic orbits of the general threebody problem by surfaces of section is introduced. The method calculates the characteristic exponents of a periodic orbit by using a nonrotating heliocentric coordinate system rather than the usual rotating coordinate system. The stability characteristics of families of resonant periodic orbits of the asteroidal type, especially of the Hecuba, Hilda and Thule groups, are analyzed. Two new families of periodic orbits with a 5:2 resonance and having the mass ratio of the SunJupiterSaturn system are found, and their stability characteristics are studied. A new type of bifurcation phenomenon in periodic orbits of the general threebody problem is discovered.
 Publication:

Ph.D. Thesis
 Pub Date:
 May 1979
 Bibcode:
 1979PhDT........41K
 Keywords:

 Orbital Mechanics;
 Three Body Problem;
 Jupiter (Planet);
 Resonance;
 Saturn (Planet);
 Sun;
 Physics (General)