Related papers: Isolating Neighborhood Trajectory Computations in …
In this paper, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in R3 and its use in the probabilistic representation of the solution of the Laplace equation with the Neumann boundary…
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
In the context of Border Gateway Protocol (BGP), inbound inter-domain traffic engineering (TE) remains a difficult problem without panacea. Each of previously investigated method solves a part of the problem. In this study, we try to…
General properties of the three-body problem in a model of modified dynamics are investigated. It is shown that the three-body problem in this model shares some characters with the similar problem in Newtonian dynamics. Moreover, the planar…
This paper presents a novel fuel-optimal guidance and control methodology for spacecraft swarm reconfiguration in Restricted Multi-Body Problems (RMBPs) with a guarantee of passive safety, maintaining miss distance even under abrupt loss of…
We present a geometric approach to the three-body problem in the non-relativistic context of the Barbour-Bertotti theories. The Riemannian metric characterizing the dynamics is analyzed in detail in terms of the relative separations.…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
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…
The multiple spacecraft guidance problem for proximity flight in libration point orbit is considered. A nonlinear optimal control problem with continuous-time path constraints enforcing minimum separation between each spacecraft is…
The discovery of interstellar interlopers such as 1I/`Oumuamua, 2I/Borisov, and 3I/ATLAS have highlighted the necessity of understanding the dynamical pathways that eject small bodies from planetary systems into hyperbolic trajectories. In…
We propose new methods for the numerical continuation of point-to-cycle connecting orbits in 3-dimensional autonomous ODE's using projection boundary conditions. In our approach, the projection boundary conditions near the cycle are…
Many bureaucratic and industrial processes involve decision points where an object can be sent to a variety of different stations based on certain preconditions. Consider for example a visa application that has needs to be checked at…
The long-term stability of the evolution of two-planet systems is considered by using the general three body problem (GTBP). Our study is focused on the stability of systems with adjacent orbits when at least one of them is highly…
The halo orbits of the spatial circular restricted three-body problem are largely considered in space-flight dynamics to design low-energy transfers between celestial bodies. A very efficient analytical method for the computation of halo…
The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion…
This study investigates the problem of traveling salesman problem with circular neighborhood (TSPCN). Instead of cities there are circles and each point on circle can be a potential visiting node. The problem is to find the minimum length…
This work addresses an extended class of optimal control problems where a target for a system state has the form of an ellipsoid rather than a fixed, single point. As a computationally affordable method for resolving the extended problem,…
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…
A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…
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…