Chapter 15. Hill's Approximation in the Three-Body Problem

Adiabatic expansion approximation solutions for the three-body problem

The motion of a muon in two centers coulomb field is one of the interesting problems of quantum mechanics. The adiabatic expansion method is powerful approach to study the muonic three-body system. In this investigation the three-body problem is studied for shortrange interactions. Bound states and energy levels of this system were calculated and compared with their Born-Oppenheimer method coun...

On Eulerian equilibria in K-order approximation of the gyrostat in the three-body problem

We consider the noncanonical Hamiltonian dynamics of a gyrostat in the three-body problem. By means of geometric-mechanics methods we study the approximate Poisson dynamics that arises when we develop the potential in series of Legendre and truncate this in an arbitrary order k. Working in the reduced problem, the existence and number of equilibria, that we denominate of Euler type in analogy w...

Three - Body Problem

Cross Sections in the Three-body Problem

In Dynamical Systems, Birkho gave a clear formulation of a cross section, suggested a possible generalization to cross sections with boundary, and raised the question of whether or not such cross sections exist in the three-body problem. In this work, we explicitly develop Birkho 's notion of a generalized cross section, formulate homological necessary conditions for the existence of a cross se...

Black Hole Binary Formation in the Expanding Universe — Three Body Problem Approximation —

We study black hole MACHO binary formation through three-body interactions in the early universe at t ∼ 10−5s . The probability distribution functions of the eccentricity and the semimajor axis of binaries as well as of the coalescence time are obtained assuming that the black holes are randomly formed in space. We confirm that the previous order-of-magnitude estimate for the binary parameters ...