Related papers: A Circular Restricted n-body Problem
In the past two decades, since the discovery of the figure-8 orbit by Chenciner and Montgomery, the variational method has became one of the most popular tools for constructing new solutions of the $N$-body problem and its extended…
In this paper we numerically explore the convergence properties of the pseudo-Newtonian circular restricted problem of three and four primary bodies. The classical Newton-Raphson iterative scheme is used for revealing the basins of…
This work addresses the problem of constrained motion control of the uncrewed surface vessels. The constraints are imposed on states/inputs of the vehicles due to the physical limitations, mission requirements, and safety considerations. We…
Trajectory design in highly-perturbed environments like binary asteroids is challenging. It typically requires using realistic, non-autonomous dynamical models in which periodic solutions derived in autonomous systems vanish. In this work,…
Transit timing variations - deviations from strict periodicity between successive passages of a transiting planet - can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for…
We present a semi-analytical correction to the seminal solution for the secular motion of a planet's orbit under gravitational influence of an external perturber derived by Heppenheimer (1978). A comparison between analytical predictions…
Planetary, stellar and galactic physics often rely on the general restricted gravitational N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted…
Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…
The circular restricted three body problem, which considers the dynamics of an infinitesimal particle in the presence of the gravitational interaction with two massive bodies moving on circular orbits about their common center of mass, is a…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an astronomical N-body system. To do this, we generalize…
Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…
Astrophysical Challenges which demand the solution of the one million (or more) gravitating body problem are briefly discussed for the fields of cosmology, galactic nuclei and globular star clusters. Results from the classical three-body…
This work is devoted to the study of some exactly solvable quantum problems of four, five and six bodies moving on the line. We solve completely the corresponding stationary Schr\"odinger equation for these systems confined in an harmonic…
We consider the Kepler two-body problem in the presence of a cosmological constant Lambda. Several dimensionless parameters characterizing the possible orbit typologies are used to identify open and closed trajectories. The qualitative…
We introduce a new particle-based hybrid code for planetary accretion. The code uses an $N$-body routine for interactions with planetary embryos while it can handle a large number of planetesimals using a super-particle approximation, in…
Planetary debris is observed in the atmospheres of over 1,000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through…
Multi-robot systems offer enhanced capability over their monolithic counterparts, but they come at a cost of increased complexity in coordination. To reduce complexity and to make the problem tractable, multi-robot motion planning (MRMP)…
The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g., a comet, asteroid, meteor or spacecraft) in the planar Sun-Jupiter…
An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…