Related papers: Trajectory Stability and Signature Diagnostics for…
In this paper, we propose a suboptimal moving horizon estimator for nonlinear systems. For the stability analysis we transfer the "feasibility-implies-stability/robustness" paradigm from model predictive control to the context of moving…
Designing for rotational stability can dramatically affect the geometry of a space station. If improperly designed, the rotating station could end up catastrophically tumbling end-over-end. Active stabilization can address this problem;…
This paper explicates the concept of an Intermediate Point (IP), its incorporation as a node along an interplanetary trajectory, and how it permits the determination and optimization of trajectories to interstellar objects (ISOs). IPs can…
Path equations of different orbiting objects in the presence of very strong gravitational fields are essential to examine the impact of its gravitational effect on the stability of each system. Implementing an analogous method, used to…
A robust drift-safe rendezvous trajectory optimization tool is developed in this work, with applications to orbital rendezvous and proximity operations. The method is based on direct collocation and utilizes a sequential convex programming…
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…
In this work, we investigate the state stabilization and trajectory tracking problems of underactuated surface ships with full state model of having non-diagonal inertia and damping matrices. By combining the novel state transformations,…
Orbital debris is a nonlinear control problem in a stratified orbital environment, not a static inventory. This paper develops a reduced-order shell-and-size framework that connects collision-rate scaling, fragment-production gain, natural…
Context: Numerous theoretical studies of the stellar dynamics of triple systems have been carried out, but fewer purely empirical studies that have addressed planetary orbits within these systems. Most of these empirical studies have been…
The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective…
In this paper we consider the problem of stabilization and tracking of desired state trajectory for a wide range of nonlinear control problems with disturbances. We present the sufficient conditions for the existence of $C^k$ state feedback…
Semi-Global Exponential Stability (SGES) is proved for the combined attitude and position rigid body motion tracking problem, which was previously only known to be asymptotically stable. Dual quaternions are used to jointly represent the…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
The cosmological dynamics are rigorously investigated through the systematic application of autonomous system analysis to the gravitational field equations in non-metricity gravity. The systematic procedure to analyze the late-time cosmic…
Low Earth Orbit (LEO) satellite mega-constellations aim to enable high-speed Internet for numerous users anywhere on Earth. To safeguard their network infrastructure in congested outer space, they perform automatic orbital maneuvers to…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
We introduce ITTO, a challenging new benchmark suite for evaluating and diagnosing the capabilities and limitations of point tracking methods. Our videos are sourced from existing datasets and egocentric real-world recordings, with…
In systems where the ability to actuate is a scarce resource, e.g., spacecrafts, it is desirable to only apply a given controller in an intermittent manner--with periods where the controller is on and periods where it is off. Motivated by…
This study provides a detailed analysis of current advancements in dynamic object tracking (DOT) and trajectory prediction (TP) methodologies, including their applications and challenges. It covers various approaches, such as feature-based,…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…