Related papers: Gauss's method for secular dynamics, softened
Evolution of self-gravitating rotating dense stellar systems (e.g. globular clusters, galactic nuclei) with embedded black holes is investigated. The interaction between the black hole and stellar component in differential rotating…
In a planetary system, a secular particle resonance occurs at a location where the precession rate of a test particle (e.g. an asteroid) matches the frequency of one of the precessional modes of the planetary system. We investigate the…
We present an analytical formalism to study the secular dynamics of a system consisting of N-2 planets orbiting a binary star in outer orbits. We introduce a canonical coordinate system and expand the disturbing function in terms of…
Disk galaxies evolve over time through processes that may rearrange both the radial mass profile and the metallicity distribution within the disk. This review of such slow changes is largely, though not entirely, restricted to…
Although the discovery of the chaotic motion of the inner planets in the solar system dates back to more than thirty years ago, the secular chaos of their orbits still dares more analytical analyses. Apart from the high-dimensional…
The long-term dynamics of the geostationary Earth orbits (GEO) is revisited through the application of canonical perturbation theory. We consider a Hamiltonian model accounting for all major perturbations: geopotential at order and degree…
Although quasi-Keplerian discs are among the most common astrophysical structures, computation of secular angular momentum transport within them routinely presents a considerable practical challenge. In this work, we investigate the secular…
Axisymmetric disks of eccentric Kepler orbits are vulnerable to an instability which causes orbits to exponentially grow in inclination, decrease in eccentricity, and cluster in their angle of pericenter. Geometrically, the disk expands to…
Numerical simulation of evolution of a cluster of a finite number of gravitating bodies interacting only by their intrinsic gravity has been carried out. The goal of the study was to reveal the main characteristic phases of the spatial…
Deep surveys conducted during the past decades have shown that galaxies in the distant universe are generally of more irregular shapes, and are disky in appearance and in their star formation rate, compared to galaxies in similar…
We construct a secular theory of a coplanar system of N-planets not involved in strong mean motion resonances, and which are far from collision zones. Besides the point-to-point Newtonian mutual interactions, we consider the general…
Self-gravitating systems evolve toward the most tightly bound configuration that is reachable via available evolution processes. The inner parts shrink and the outer parts expand, provided that some physical process transports energy or…
We describe the long-term evolution of compact systems of terrestrial planets, using a set of simulations that match the statistical properties of the observed exoplanet distribution. The evolution is driven by tidal dissipation in the…
One of the major obstacles to testing alternative theories of gravity with gravitational-wave data from merging binaries of compact objects is the formulation of their field equations, which is often mathematically ill-suited for time…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
We present a theory in three parts, of the secular dynamics of a (Keplerian) stellar system of mass $M$ orbiting a black hole of mass $M_\bullet \gg M$. Here we describe the collisionless dynamics; Papers II and III are on the (collisional)…
This study focuses on the long-term evolution of two bodies in nearby initially coplanar orbits around a central dominant body perturbed by a fourth body on a distant Keplerian orbit. Our previous works that considered this setup enforced…
We present a new two-fluid conduction scheme to simulate the evolution of an isolated, self-gravitating, equilibrium cluster of stars and collisionless dark matter on secular (gravothermal) timescales. We integrate the equations in…
We present gravitational N-body simulations of the secular morphological evolution of disk galaxies induced by density wave modes. In particular, we address the demands collective effects place on the choice of simulation parameters, and…
In many astrophysical problems involving discs (gaseous or particulate) orbiting a dominant central mass, gravitational potential of the disc plays an important dynamical role. Its impact on the motion of external objects, as well as on the…