Related papers: On the perturbed harmonic oscillator and celestial…
The classical disturbing function of the three-body problem widely used in planetary dynamics studies is an expansion of the gravitational interaction of the three-body problem with respect to zero eccentricity and zero inclination. This…
The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an…
One-armed oscillation modes in the circumstellar discs of Be stars may explain the cyclical variations in their emission lines. We show that a three-dimensional effect, involving vertical motion and neglected in previous treatments,…
We studied the orbit of an electron revolving around an infinitely massive nucleus of a large classical Hydrogen atom subject to an AC electric field oscillating perpendicular to the electron's circular orbit. Using perturbation theory in…
The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these…
This paper investigates the secular motion of a massless asteroid within the framework of the double-averaged elliptic restricted three-body problem. By employing Poincar\'e variables, we analyze the stability properties of asteroid orbits…
It is shown that the curvature of spacetime, a possible net electric charge on the sun, a small positive cosmological constant and the oblateness of the sun, in conjunction with solar radiation pressure (SPR), affect the bound orbital…
In this paper, we provide a systematic investigation of high-order primordial perturbations with nonlinear dispersion relations due to quantum gravitational effects in the framework of {\em uniform asymptotic approximations}. Because of…
A framework was recently proposed for doing perturbation theory on noncommutative (NC) spacetime. It preserves the unitarity of S matrix and differs from the naive, popular approach already at the lowest order in perturbation when time does…
We derive octupole-level secular perturbation equations for hierarchical triple systems, using classical Hamiltonian perturbation techniques. By extending previous work done to leading (quadrupole) order to octupole level (i.e., including…
We consider an axi-symmetric rotor perturbed by dissipative, conservative, and non-conservative positional forces originated at the contact with the anisotropic stator. The Campbell diagram of the unperturbed system is a mesh-like structure…
We revisit the connection between relativistic orbital precession, the Laplace-Runge-Lenz symmetry, and the $t$-channel discontinuity of scattering amplitudes. Applying this to scalar-tensor theories of gravity, we compute the conservative…
Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum…
In galaxy-galaxy strong gravitational lensing, Einstein rings are generated when the lensing galaxy has an axisymmetric lensing potential and the source galaxy is aligned with its symmetry centre along the line of sight. Using a Taylor…
In this thesis, we discuss several instances in which non-linear behaviour affects cosmological evolution in the early Universe. We begin by reviewing the standard cosmological model and the tools used to understand it theoretically and to…
Stars bound to a supermassive black hole interact gravitationally. Persistent torques acting between stellar orbits lead to the rapid resonant relaxation of the orbital orientation vectors ("vector" resonant relaxation) and slower…
We consider the physics of free precession of a rotating neutron star with an oblique magnetic field. We show that if the magnetic stresses are large enough, then there is no possibility of steady rotation, and precession is inevitable.…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
We demonstrate the existence of an enhanced rate of angular momentum relaxation in nearly Keplerian star clusters, such as those found in the centers of galactic nuclei containing massive black holes. The enhanced relaxation arises because…
In Ref. [1, 2] a formalism to deal with high-order perturbations of a general spherical background was developed. In this article, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the…