Related papers: A surface constraint approach for solar sail orbit…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…
We study some aspects of the geometric side of the Jacquet-Rallis relative trace formula. Globally, we compute each geometric term of the Jacquet-Rallis relative trace formula on the general linear group for regular supported test…
Recent work in the literature has advocated using the Earth-Moon-planetoid Lagrangian points as observables, in order to test general relativity and effective field theories of gravity in the solar system. However, since the three-body…
A stationary rotating surface is a compact surface in Euclidean space whose mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are constants.…
General relativity can have a significant impact on the long-range escape trajectories of solar sails deployed near the sun. Spacetime curvature in the vicinity of the sun can cause a solar sail traveling from 0.01 AU to 2550 AU to be…
We calculate, up to the first-order in the black hole spin, the perihelion precession of a test particle in the equatorial plane of a Kerr black hole using the perturbative Laplace-Runge-Lenz (LRL) vector method. To account for the dragging…
This paper develops a robust angles-only IROD method based on polynomial optimization for arbitrary nonlinear dynamics. First, the relative motion is approximated by high-order Taylor polynomials within the differential algebra framework,…
The paper studies the problem of making Getz's bicycle model traverse a strictly convex Jordan curve with bounded roll angle and bounded speed. The approach to solving this problem is based on the virtual holonomic constraint (VHC) method.…
We present an approach to enhance wheeled planetary rover dead-reckoning localization performance by leveraging the use of zero-type constraint equations in the navigation filter. Without external aiding, inertial navigation solutions…
Surface geometry plays a central role in the design of bridges, vaults and shells, using various techniques for generating a geometry which aims to balance structural, spatial, aesthetic and construction requirements. In this paper we…
A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the…
Contraction analysis uses a local criterion to prove the long-term behaviour of a dynamical system. A contraction metric is a Riemannian metric with respect to which the distance between adjacent solutions contracts. If adjacent solutions…
Solar sails enable missions to observe the solar environment from unique vantage points, such as sustained observations away from the Sun-Earth line; sub-L1 station keeping; high inclination solar orbits; Earth polar-sitting and…
In this paper an inverse preconditioner for the numerical solution of an elliptic Laplace prob- lem of a global circulation ocean model is presented. The inverse preconditiong technique is adopted in order to efficiently compute the…
The objective of this work is to demonstrate the utility of Lyapunov functions in control synthesis for the purpose of maintaining and stabilizing a spacecraft in a circular orbit around the L4 point in the circular restricted three body…
Simulating curvature due to gravity through warped surfaces is a common visualization aid in Physics education. We reprise a recent experiment exploring orbital trajectories on a precise 3D-printed surface to mimic Newtonian gravity, and…
The rapid increase in the deployment of Low Earth Orbit (LEO) satellites, catering to diverse applications such as communication, Earth observation, environmental monitoring, and scientific research, has significantly amplified the…
By tooling an spot-illuminated surface to control the flow of specular glints under motion, one can produce holographic view-dependent imagery. This paper presents the differential equation that governs the shape of the specular surfaces,…
There are many indications that anthropogenic global warming poses a serious threat to our civilization and its ecological support systems. Ideally this problem will be overcome by reducing greenhouse gas emissions. Various space-based…
Traditional lens design is a numerical and forward process based on ray tracing and aberration theory. This method has limitations because the initial configuration of the lens has to be specified and the aberrations of the lenses have to…