Related papers: Circular and Elliptic Restricted Three Body Proble…
The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian config- uration of the three-body problem, i,e,. they remain fixed at the apices of an equilateral…
We consider the planar three body problem of planetary type and we study the generation and continuation of periodic orbits and mainly of asymmetric periodic orbits. Asymmetric orbits exist in the restricted circular three body problem only…
We compare three approaches to posing the index 3 set of differential algebraic equations (DAEs) associated with the constrained multibody dynamics problem formulated in absolute coordinates. The first approach works directly with the…
Three body systems where one of the bodies is ejected without escaping the binary system have previously been studied in various restricted forms. However, none of these studies dwells on the problem in a general setting. Thus, to study…
In this paper, we consider the elliptic relative equilibria of the restricted $4$-body problems, where the three primaries form an Euler collinear configuration and the four bodies span $\mathbf{R}^2$. We obtain the symplectic reduction to…
The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian configuration of the three-body problem i.e., they remain fixed at the apices of an equilateral…
In this paper we consider the planar circular restricted three body problem (PCRTBP), which models the motion of a massless body under the attraction of other two bodies, the primaries, which describe circular orbits around their common…
In this paper, we consider the elliptic relative equilibria of the restricted $N$-body problems, where the $N-1$ primaries form an Euler-Moulton collinear central configuration or a $(1+n)$-gon central configuration. We obtain the…
Consider the Restricted Planar Circular 3 Body Problem with both realistic mass ratio and Jacobi constant for the Sun-Jupiter pair. We prove the existence of all possible combinations of past and future final motions. In particular, we…
The rectilinear elliptic restricted Three Body Problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity $e'=1$, but the collision of the…
Isolating block and isolating neighborhood methods have previously been implemented to find transit trajectories and orbits around libration points in the autonomous circular restricted three-body problem. For some applications, the direct…
We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability…
We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2,…
We carry out a sequence of coordinate changes for the planar three-body problem which successively eliminate the translation and rotation symmetries, regularize all three double collision singularities and blow-up the triple collision.…
We consider the special case of the restricted circular three-body problem, when the two primaries are of equal mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the…
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid…
We consider the planar circular equilateral restricted four body-problem where a test particle of infinitesimal mass is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common…
This paper considers two point boundary value problems for conservative systems defined in multiple coordinate systems, and develops a flexible a-posteriori framework for computer assisted existence proofs. Our framework is applied to the…
Optimal control problems are formulated and efficient computational procedures are proposed for combined orbital and rotational maneuvers of a rigid body in three dimensions. The rigid body is assumed to act under the influence of forces…
We consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three "radial" and three angular variables, which determine the shape and…