Adiabatic invariants and phase equilibria for first-order orbital resonances

Details Adiabatic invariants and phase equilibria for first-order orbital resonances Adiabatic invariants and phase equilibria for first-order orbital resonances

Jun 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975aj.....80..465h&link_type=abstract

Astronomical Journal, vol. 80, June 1975, p. 465-472.

Astronomy and Astrophysics

Astronomy

4

Asteroids, Lagrangian Equilibrium Points, Mass Ratios, Orbit Perturbation, Orbital Resonances (Celestial Mechanics), Solar Orbits, Three Body Problem, Adiabatic Equations, Boundary Value Problems, Circular Orbits, Libration, Numerical Integration, Orbit Calculation, Phase-Space Integral, Solar System, Stellar Mass Ejection, Variational Principles

Scientific paper

In the planar circular restricted three-body problem, the evolution of near-commensurable orbits is studied under change in the mass ratio, mu. The evolution involves preservation of two adiabatic invariants. Transition from circulation to libration may occur; such transitions are of two types. Type I transition occurs when the evolutionary track in phase space passes through near-zero eccentricity; as in the ordinary case (no transition), pre- and post-evolutionary states are linked by solution of a two-point boundary-value problem. Type II transition occurs when the evolutionary track encounters an unstable phase equilibrium or periodic orbit. There is then a discontinuous change in one adiabatic invariant, and pre- and post-evolutionary states are linked by solution of a three-point boundary-value problem. No evolutionary track can encounter a stable phase equilibrium, but the class of all stable phase equilibria is mapped into itself under mu change.

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