Applications of singular perturbation theory to the restricted three body problem

Aas 12-189 Canonical Perturbation Theory for the Elliptic Restricted-three-body Problem

The distinguishing characteristic of the elliptic restricted three-body problem is a time-varying potential field resulting in non-autonomous and non-integrable dynamics. The purpose of this study is to normalize the system dynamics about the circular case and about one of the triangular Lagrange points by applying a method of canonical perturbation theory introduced by Hori and Deprit in the 1...

Singular Cores in the Three - Body Problem I : Theory

The three-body formalism for singular cores previously introduced by the author is considered in some detail. A new derivation is presented which clearly demonstrates the uniqueness of this formalism, and a detailed proof of threeparticle unitarity is given for the amplitudes so defined. The kernel for the special case of BCM alone is explicitly evaluated, and the result is used to analyze some...

Caustics of the restricted three-body problem

Trajectories of the planar, circular, restricted threebody problem are given in the configuration space through the caustics associated to the invariant tori of quasi-periodic orbits. It is shown that the caustics of trajectories librating in any particular resonance display some features associated to that resonance. This method can be considered complementary to the Poincaré surface of sectio...

Singular perturbation theory

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...

Geometric Singular Perturbation Theory