The Stability Parameters of ThreeBody Periodic Orbits
Abstract
Formulae containing the elements of the variational matrix are obtained which determine the linear ‘isoenergetic’ stability parameters of periodic orbits of the general threebody problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The procedure is applied for the determination of ‘horizontally’ critical orbits among the members of sets of verticalcritical periodic orbits of the threebody problem. These ‘criticalcritical’ orbits have special importance as they delimit the regions in the space of initial conditions which correspond to possibly stable threedimensional periodic motion of low inclination.
 Publication:

Earth Moon and Planets
 Pub Date:
 July 1988
 DOI:
 10.1007/BF00118041
 Bibcode:
 1988EM&P...42...61P
 Keywords:

 Motion Stability;
 Orbital Mechanics;
 Three Body Problem;
 Isoenergetic Processes;
 Matrices (Mathematics);
 Numerical Integration;
 Astrophysics