Families of Periodic Orbits in the Planar Problem of Three Bodies.
Abstract
The linear stability of families was examined using the variational equations in both heliocentric and Jacobian coordinate systems. Stable and unstable orbits were found as the ratio of the masses goes from the restricted problem to the equal mass case. Stability of orbits having close approaches or collisions was examined. A parameter that is the product of the square of the angular momentum and the total energy was computed for orbits in each family. This parameter was compared to the critical values obtained from the zero velocity surfaces of the planar problem of three bodies to obtain a measure of stability. The orbits are computed with a RungeKuttaFehlberg numerical integrator using the regularization method of LeviCivita.
 Publication:

Ph.D. Thesis
 Pub Date:
 1977
 Bibcode:
 1977PhDT........10D
 Keywords:

 Physics: Astronomy and Astrophysics;
 Orbits;
 Three Body Problem;
 Variational Principles;
 Calculus Of Variations;
 Jacobi Matrix Method;
 Linearity;
 Numerical Integration;
 RungeKutta Method;
 Stability;
 Astrophysics