Non-schubart periodic orbits in the rectilinear three-body problem

Abstract

In the present paper, in the rectilinear three-body problem, we qualitatively follow the positions of non-Schubart periodic orbits as the mass parameter changes. This is done by constructing their characteristic curves. In order to construct characteristic curves, we assume a set of properties on the shape of areas corresponding to symbol sequences. These properties are assured by our preceding numerical calculations. The main result is that characteristic curves always start at triple collision and end at triple collision. This may give us some insight into the nature of periodic orbits in the N -body problem.

A new collision-based periodic orbit in the three-dimensional eight-body problem

“…Existence, stability, and other properties of periodic orbits with three bodies in one spatial dimension are studied in both analytical and numerical contexts as early as 1956 in [28] and as recently as 2019 in [13]. Works between these years include [10], [11], [25], [18], [33], [26], [27], [29], [37], and [21]. Orbits with four bodies in one spatial dimension are featured in [29], [15], [12] and [35].…”

The Eight-Body Cubic Collision-Based Periodic Orbit

“…Existence, stability, and other properties of periodic orbits with three bodies in one spatial dimension are studied in both analytical and numerical contexts as early as 1956 in [28] and as recently as 2019 in [13]. Works between these years include [10], [11], [25], [18], [32], [26], [27], [29], [35], and [21]. Orbits with four bodies in one spatial dimension are featured in [29], [15], [12] and [33].…”

Linear stability analysis of symmetric periodic simultaneous binary collision orbits in the planar pairwise symmetric four-body problem

“…These are linearly stable for certain choices of the three masses [5]. Linearly stable non-Schubart orbits have also been found in the collinear three-body problem for certain choices of the masses [11], [12], [13]. The Schubart-like orbit in the collinear symmetric four-body problem [18], [19], [14], [9], [17], alternates between a binary collision of the two inner bodies and a SBC of the two outer pairs of bodies.…”