Related papers: A Two-Dimensional Analytic Solution for the Genera…
This article presents a new algorithm, the Hyperbolic and Elliptic Points Tracking Algorithm (HEPTA), designed for automated tracking of elliptic and hyperbolic stationary points in two-dimensional non-stationary velocity fields defined on…
Solar system, exoplanet and stellar science rely on transits, eclipses and occultations for dynamical and physical insight. Often, the geometry of these configurations are modelled by assuming a particular viewpoint. Here, instead, I derive…
The dynamics of a test particle in a non-spinning binary black hole system of equal masses is numerically investigated. The binary system is modeled in the context of the pseudo-Newtonian circular restricted three-body problem, such that…
We derive the secular evolution of the orbital elements of a stellar-mass object orbiting a spinning massive black hole. We use the post-Newtonian approximation in harmonic coordinates, with test-body equations of motion for the…
In this article, we consider a class of strictly hyperbolic triangular systems involving a transport equation. Such systems are known to create measure solutions for the initial value problem. Adding a stronger transversality assumption on…
We analyze the behavior of the argument of pericenter $\omega_2$ of an outer particle in the elliptical restricted three-body problem, focusing on the inverse Lidov-Kozai resonance. First, we calculate the contribution of the terms of…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
The specific objective of this paper is to develop a tool that calculates the optimal trajectory of the follower aircraft as it completes a formation rejoin, and then maintains the formation position, defined as a ring of points, until a…
For the well-known model of a system of N particles with interaction (N-body problem), we consider the spatial problem of finding the minimum of the function of the kinetic energy of a system on its phase space under conditions on its size…
The $N$-body problem is of historical significance because it was the first implementation of the Newtonian dynamical laws for the description of our Solar System. Motivated by this, the project's goal is to revisit this problem for small…
We study the bifurcation structure of highly inclined near halo orbits with close approaches to the light primary, in the circular restricted three-body problem (CR3BP). Using a Hamiltonian formulation together with Moser regularization, we…
We develop a formalism for calculating probabilities for the outcomes of stellar dynamical interactions, based on results from $N$-body scattering experiments. We focus here on encounters involving up to six particles and calculate…
This study uses a combination of stochastic optimization, statistical mechanical theory, and molecular simulation to test the extent to which the long-time dynamics of a single tracer particle can be enhanced by rationally modifying its…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
Interstellar objects (ISOs) motivate a coupled mission-design and inference question relevant to spacecraft dynamics and control in extreme environments: if volatile-rich, rotating comet-like bodies were used for sustained deep-space…
As low-thrust space missions increase in prevalence, it is becoming increasingly important to design robust trajectories against unforeseen thruster outages or missed thrust events. Accounting for such events is particularly important in…
We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional…
We study an intrinsic model for collective behaviour on the hyperbolic space $\bbh^\dm$. We investigate the equilibria of the aggregation equation (or equivalently, the critical points of the associated interaction energy) for interaction…
This paper presents a method to determine the reachable set (RS) of spacecraft after a single velocity impulse with an arbitrary direction, which is appropriate for the RS in both the state and observation spaces under arbitrary dynamics,…
1I/'Oumuamua (or 1I) and 2I/Borisov (or 2I), the first InterStellar Objects (ISOs) discovered passing through the solar system, have opened up entirely new areas of exobody research. Finding additional ISOs and planning missions to…