Related papers: Stability criteria for hierarchical triple systems
We study the dynamical stability of self-gravitating systems in presence of anisotropy. In particular, we introduce a stability criterion, in terms of the adiabatic local index, that generalizes the stability condition $<\gamma> \geq 4/3$…
This paper presents an approach to deal with safety of dynamical systems in presence of multiple non-convex unsafe sets. While optimal control and model predictive control strategies can be employed in these scenarios, they suffer from high…
We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
In this paper, we derive differential conditions guaranteeing the orbital stability of nonlinear hybrid limit cycles. These conditions are represented as a series of pointwise linear matrix inequalities (LMI), enabling the search for…
The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a…
We introduce a framework for the description of a large class of delay-differential algebraic systems, in which we study three core problems: first we characterize abstractly the well-posedness of the initial-value problem, then we design a…
We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from Control Theory to…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…
We present numerical simulations of the gravitational three-body problem, in which three particles lie at rest close to the vertices of an equilateral triangle. In the unperturbed problem, the three particles fall towards the center of mass…
We study the effects of general relativistic gravity on the Hill stability, that is, the stability of a multi-body system against a close approach of one orbit to another, which has been hitherto studied mainly in Newtonian mechanics and…
This paper presents a study of the use of numerical simulation and Bayesian optimisation techniques to investigate the dynamics of celestial systems. Initially, the study focuses on Lagrange points in restricted three-body systems where a…
We discuss the stability of three- and four-particle system interacting by pure Coulomb interactions, as a function of the masses and charges of the particles. We present a certain number of general properties which allow to answer a…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
This paper studies robustness of MIMO control systems with parametric uncertainties, and establishes a lower dimensional robust stability criterion. For control systems with interval transfer matrices, we identify the minimal testing set…
This study examines the dynamics of the third body in an elliptic restricted three-body problem (ERTBP) framework, taking into account perturbations from radiation pressure, oblateness, and elongation of the primary bodies, as well as…
Hysteresis can be defined from a dynamical systems perspective with respect to equilibrium points. Consequently, hysteresis naturally lends itself as a topic to illustrate and extend concepts in a dynamical systems course. A number of…
In this paper, we provide an overview of the research conducted in the context of structural systems since the latest survey by Dion et al. in 2003. We systematically consider all the papers that cite this survey as well as the seminal work…