Related papers: A Rapid Method For Orbital Coverage Statistics Wit…
By definition, a map quasiperiodic on a set $X$ if the map is conjugate to a pure rotation. Suppose we have a trajectory $(x_n)$ that we suspect is quasiperiodic. How do we determine if it is? In this paper we show how to compute the…
We apply the MEGNO (Mean Exponential Growth of Nearby Orbits) technique to the dynamics of Jovian irregular satellites. We demonstrate the efficiency of applying the MEGNO indicator to generate a mapping of relevant phase-space regions…
A novel fast multi-impulse optimization method for long-duration perturbed orbit rendezvous is proposed. First, based on the analytically estimated impulses, the terminal rendezvous deviation with precise dynamics model can be predicted.…
This paper shows how the application of stochastic geometry to the analysis of wireless networks is greatly facilitated by (i) a clear separation of time scales, (ii) the abstraction of small-scale effects via ergodicity, and (iii) an…
In nominal mission scenarios, geostationary satellites perform end-of-life orbit maneuvers to reach suitable disposal orbits, where they do not interfere with operational satellites. This research investigates the long-term orbit evolution…
Ergodic exploration has spawned a lot of interest in mobile robotics due to its ability to design time trajectories that match desired spatial coverage statistics. However, current ergodic approaches are for continuous spaces, which require…
The impact of mega-constellations of satellites in low-Earth orbit during nighttime optical observations is assessed. Orbital geometry is used to calculate the impact of stellar occultations by satellites on the photometry of individual…
Orbital parameters of planets are fitted directly to an appropriate set of observations. It is shown how to use the rigorous Deming method combined with a numerical integration of gravitation equations. In all, 65 parameters of the nine…
A general theory of efficient estimation for ergodic diffusion processes sampled at high frequency with an infinite time horizon is presented. High frequency sampling is common in many applications, with finance as a prominent example. The…
We develop two general methods to infer the gravitational potential of a system using steady-state tracers, i.e., tracers with a time-independent phase-space distribution. Combined with the phase-space continuity equation, the time…
To mitigate inter-satellite interference and payload limits in LEO mega-constellations, satellite clusters, groups of small cooperative satellites have been proposed to improve performance and reduce interference. The typical configuration…
In recent years, LEO satellite constellations have become envisioned as a core component of the next-generation wireless communication networks. The successive establishment of mega satellite constellations has triggered further demands for…
Low Earth orbit (LEO) satellites are being considered for expanding legacy terrestrial cellular networks. The end users may not be able to optimize satellite orbits and constellations, however, they can optimize locations of ground stations…
Topical observations of the thermosphere at altitudes below $200 \, km$ are of great benefit in advancing the understanding of the global distribution of mass, composition, and dynamical responses to geomagnetic forcing, and momentum…
A significant fraction of an exoplanet transit model evaluation time is spent calculating projected distances between the planet and its host star. This is a relatively fast operation for a circular orbit, but slower for an eccentric one.…
We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…
Preliminary mission design requires an efficient and accurate approximation to the low-thrust rendezvous trajectories, which might be generally three-dimensional and involve multiple revolutions. In this paper, a new shaping method using…
Low Earth orbit (LEO) satellite networks with mega constellations have the potential to provide 5G and beyond services ubiquitously. However, these networks may introduce mutual interference to both satellite and terrestrial networks,…
Exploration requires that robots reason about numerous ways to cover a space in response to dynamically changing conditions. However, in continuous domains there are potentially infinitely many options for robots to explore which can prove…
We present a novel formulation of ergodic trajectory optimization that can be specified over general domains using kernel maximum mean discrepancy. Ergodic trajectory optimization is an effective approach that generates coverage paths for…