Orbits near a 2/3 resonance
Abstract
Orbits in a galactictype potential are investigated for the case of values of the coefficients of the position coordinates specifying a near 2/3 resonance. The theory of Lie transforms is used to reduce the Hamiltonian of the potential in canonical form, and the coefficients of the third integral are determined up to the 14th degree, resulting in expressions for the characteristics of the theoretical periodic orbits. The properties of several nonperiodic orbits are calculated as well to obtain the rotation number as a function of distance from the central nonperiodic orbit, and the characteristics of the various families of periodic orbits, which intersect the x axis perpendicularly up to 14 times, are examined. Finally, the empirically derived rotation numbers are compared with those derived theoretically, and invariant and rotation curves within the potential are illustrated for selected values of the coefficient of the term coupling the position coordinates.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 November 1980
 Bibcode:
 1980A&A....91..165M
 Keywords:

 Orbit Calculation;
 Orbital Mechanics;
 Orbital Resonances (Celestial Mechanics);
 Periodic Variations;
 Resonance;
 Stellar Motions;
 Astronomical Coordinates;
 Canonical Forms;
 Computer Programs;
 Galactic Rotation;
 Hamiltonian Functions;
 Lie Groups;
 Astronomy