Related papers: Hill stability in the AMD framework

Motivated by a class of orbit problems in astrophysics, this paper considers solutions to Hill's equation with forcing strength parameters that vary from cycle to cycle. The results are generalized to include period variations from cycle to…

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…

We establish the Hyers-Ulam stability of a second-order linear Hill-type $h$-difference equation with a periodic coefficient. Using results from first-order $h$-difference equations with periodic coefficient of arbitrary order, both…

The orbits in the HD 160691 planetary system at first appeared highly unstable, but using the MEGNO and FLI techniques of global dynamics analysis in the orbital parameter space we have found a stabilizing mechanism that could be the key to…

Anyone who has built a sandcastle recognizes that the addition of liquid to granular materials increases their stability. However, measurements of this increased stability often conflict with theory and with each other [1-7]. A…

This paper presents a deterministic hybrid observer for the attitude dynamics of a rigid body that guarantees global asymptotical stability. Any smooth attitude observer suffers from the inherent topological restriction that it is…

The majority of star formation results in binaries or higher multiple systems, and planets in such systems are constrained to a limited range of orbital parameters in order to remain stable against perturbations from stellar companions.…

We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape…

Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological…

Applying the technique of dynamical maps we study the orbital stability of test particles in the Solar System in the space (a,e,i) defined by 0.1<a<38 au, 0<e<0.9 and 0<i<180 identifying the unstable and stable regions. We find stable…

Because of the high eccentricities (~0.3) of two of the possible planets about the star Upsilon Andromeda, the stability of the system requires careful study. We present results of 1000 numerical simulations which explore the orbital…

It is well established that certain detached eclipsing binary stars exhibit apsidal motions whose value is in disagreement with with calculated deviations from Keplerian motion based on tidal effects and the general theory of relativity.…

We have numerically explored the stable planetary geometry for the multiple systems involved in a 2:1 mean motion resonance, and herein we mainly study the HD 82943 system by employing two sets of the orbital parameters (Mayor et al. 2004;…

Birkhoff normal forms are commonly used in order to ensure the so called "effective stability" in the neighborhood of elliptic equilibrium points for Hamiltonian systems. From a theoretical point of view, this means that the eventual…

We provide a version of Quillen's homological stability criterion for continuous bounded cohomology. This criterion is exploited in the companion paper (arXiv:2201.03879) in order to derive new bounded cohomological stability results for…

(Abridged) We have numerically explored the stable planetary geometry for the multiple systems involved in a 2:1 mean motion resonance, and herein we mainly concentrate on the study of the HD 82943 system by employing two sets of the…

We present a detailed analysis of the orbital stability of the HD 181433 planetary system, finding it to exhibit strong dynamical instability across a wide range of orbital eccentricities, semi-major axes, and mutual inclinations. We also…

Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…

Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…

Context: Seasonal variations and climate stability of a planet are very sensitive to the planet obliquity and its evolution. This is of particular interest for the emergence and sustainability of land-based life, but orbital and rotational…