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Related papers: Stability criteria for hierarchical triple systems

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Stability is one of the most fundamental aspects regarding planetary systems. It plays an important role in our understanding on the formation channel of the planetary systems, as well as their habitability. Many approaches have been…

Earth and Planetary Astrophysics · Physics 2024-07-22 Hareesh Gautham Bhaskar , Nathaniel W. H. Moore , Jiapeng Gao , Gongjie Li , Billy Quarles

A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…

Dynamical Systems · Mathematics 2019-04-01 Björn Lindenberg

A recently proposed connection between the threshold for the stability of the iterative solution of integral equations for the pair correlation functions of a classical fluid and the structural instability of the corresponding real fluid is…

Condensed Matter · Physics 2009-11-10 R. Fantoni , G. Pastore

In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We carry out more than 3 10^8 numerical simulations of planets between the size of Mercury and…

Earth and Planetary Astrophysics · Physics 2024-09-06 Nikolaos Georgakarakos , Siegfried Eggl , Mohamad Ali-Dib , Ian Dobbs-Dixon

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…

Optimization and Control · Mathematics 2008-06-23 Luca Scardovi , Naomi Leonard , Rodolphe Sepulchre

This paper proposes a novel method for determining the number of factors in linear factor models under stability considerations. An instability measure is proposed based on the principal angle between the estimated loading spaces obtained…

Methodology · Statistics 2024-09-13 Sze Ming Lee , Yunxiao Chen

For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equilibria of exactly one of the two neighbouring pieces of the…

Dynamical Systems · Mathematics 2026-02-10 David J. W. Simpson

Based on the generalized Routh-Hurwitz criterion, we propose a sufficient and necessary criterion for testing the stability of fractional-order linear systems with order {\alpha}{\in}[1,2), called the fractional-order Routh-Hurwitz…

Dynamical Systems · Mathematics 2022-02-22 Jing Yang , Xiaorong Hou , Yajun Li

In this short note we prove a hierarchical stability result that applies to hybrid dynamical systems satisfying the hybrid basic conditions of (Goebel et al., 2012). In particular, we establish sufficient conditions for uniform asymptotic…

Systems and Control · Computer Science 2016-01-07 Mario Sassano , Luca Zaccarian

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

Dynamical Systems · Mathematics 2020-12-29 Mark A. Pinsky

A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…

Machine Learning · Statistics 2010-07-08 Ulrike von Luxburg

We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…

Quantum Physics · Physics 2023-05-31 Xuanloc Leu , Xuan-Hoai Thi Nguyen , Jinhyoung Lee

Goal of the presented research is to construct simplified model of the core-halo structures in binary systems. Examples are provided by Thorne-Zytkov objects, hot Jupiters, protoplanets with large moons, red supergiants in binaries and…

Solar and Stellar Astrophysics · Physics 2016-09-02 A. Odrzywolek

An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…

Systems and Control · Electrical Eng. & Systems 2024-11-22 Simone Mariano , Michael Cantoni

We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability…

General Relativity and Quantum Cosmology · Physics 2016-03-16 M. Abishev , H. Quevedo , S. Toktarbay , B. Zhami

The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid's bus angles to retain synchronism after the occurrence of a major fault. In this paper a…

Optimization and Control · Mathematics 2021-01-12 Tim Aschenbruck , Willem Esterhuizen , Stefan Streif

We consider here a recently proposed geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Alberto Saa

The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to…

Metric Geometry · Mathematics 2025-06-30 Zeyuan He

This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…

Machine Learning · Computer Science 2024-03-04 Igor Pontes Duff , Pawan Goyal , Peter Benner

In a series of papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. However, for certain combinations of the masses and the orbital elements,…

Astrophysics · Physics 2009-11-13 Nikolaos Georgakarakos