Euler integral as a source of chaos in the three–body problem

Numerical studies to detect chaotic motion in the full planar averaged three-body problem

“…At the same time, the problem has been studied from a numerical point of view in order to prove existence of chaotic motions under particular initial configurations. We refer, in particular to papers [8,9].…”

“…The purpose of the current paper is to collect and to link two recent works (we refer to papers [8,9]) where the onset of chaos is numerically proved in two different configurations of the three-body problem. In both the works, we aim to write the Hamiltonian describing the model as the sum of a Keplerian part ruling the motion of two of three bodies plus a part depending on all the three bodies.…”

“…In works [8,9], two different configurations and phase-spaces are considered and in both cases we use symbolic dynamics to prove, numerically, the existence of chaotic motions. In Sect.…”

“…Indeed, the goal of the current paper is to show a method to apply to the perturbed Keplerian problem when some conditions are satisfied. Afterwards, the two different cases of papers [8,9] are described.…”

Chaotic coexistence of librational and rotational dynamics in the averaged planar three--body problem

“…We specify that we deal with the Hamiltonian of the full three-body problem, where "full" is used as opposed to the so-called "restricted" problem; thus, the three bodies have no negligible masses and the motion of each one is ruled by mutual Newtonian gravitational attraction. The idea, already used in previous articles such as [3,4,6,7] and coming from papers [19][20][21] is to consider, in principle, no Newtonian interaction between the three bodies as dominant. We use new coordinates (see [19]) associated to the three bodies and through suitable rescalings of variables and time we write the new Hamiltonian describing the model as the sum of a Keplerian part ruling the motion of two of three bodies plus a part depending on all the three bodies.…”