相关论文: Correlation of macroscopic instability and Lyapuno…
In this study we consider the relationship between the survival time and the Lyapunov time for 3-body systems. It is shown that the Sitnikov problem exhibits a two-part power law relationship as demonstrated previously for the general…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
We consider statistics of the disruption and Lyapunov times in an hierarchical restricted three-body problem. We show that at the edge of disruption the orbital periods and the size of the orbit of the escaping body exhibit L\'evy flights.…
We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms…
The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital…
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…
Chaos indicators, like the Lyapunov exponent lambda, are widely used in celestial mechanics to characterize the dynamical behavior of bodies. The stability of their orbit can be determined by the calculation of the local exponential…
In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to…
The restricted three body problem is well-known and very important for dynamics of binary, multiple stars and also planetary systems. We extend the classical version of this problem to the situation that there are some external forces from…
We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is…
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…
Recent numerical results seem to suggest that in certain regimes of typical particle velocities the gravitational $N-$body problem (for $3\leq N\lesssim 10^3$) is intrinsically less chaotic when the post-Newtonian (PN) force terms are…
We develop an extension of the fast method of angles for hyperbolicity verification in chaotic systems with an arbitrary number of time-delay feedback loops. The adopted method is based on the theory of covariant Lyapunov vectors and…
In the present paper, which is a development of an earlier study by the author \cite{Sosnitskii08}, we consider the stability of triangular libration points in the spatial circular restricted three-body problem and improve the result of…
While there have been many studies examining the stability of hierarchical triple systems, the meaning of ``stability'' is somewhat vague and has been interpreted differently in previous literatures. The present paper focuses on ``Lagrange…
We investigate the predictability problem in dynamical systems with many degrees of freedom and a wide spectrum of temporal scales. In particular, we study the case of $3D$ turbulence at high Reynolds numbers by introducing a finite-size…
We consider the planar circular restricted three-body problem (PCRTBP), as a model for the motion of a spacecraft relative to the Earth-Moon system. We focus on the Lagrange equilibrium points $L_1$ and $L_2$. There are families of Lyapunov…
Instabilities in compact planetary systems are generically driven by chaotic dynamics. This implies that an instability time measured through direct N-body integration is not exact, but rather represents a single draw from a distribution of…
The classical three-body harmonic system in $\mathbb{R}^d$ ($d>1$) with finite rest lengths and zero total angular momentum $L=0$ is considered. This model describes the dynamics of the $L=0$ near-equilibrium configurations of three point…
Numerical integrations of the closely-packed inner Uranian satellite system show that variations in semi-major axes can take place simultaneously between three or four consecutive satellites. We find that the three-body Laplace angle values…