Related papers: Analytical theory for highly elliptical orbits inc…
As periodic orbit theory works badly on computing the observable averages of dynamical systems with intermittency, we propose a scheme to cooperate with cycle expansion and perturbation theory so that we can deal with intermittent systems…
We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration…
Asymptotic methods in nonlinear dynamics are used to improve perturbation theory results in the oscillations regime. However, for some problems of nonlinear dynamics, particularly in the case of Higgs (Duffing) equation and the Friedmann…
We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor-Hoenselaers-Perj\'es procedure, we perform an expansion in the mass potential of a static…
A test particle in a noncoplanar orbit about a member of a binary system can undergo Kozai-Lidov oscillations in which tilt and eccentricity are exchanged. An initially circular highly inclined particle orbit can reach high eccentricity. We…
Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of 'stationary' multiple time-scale systems which possess a critical manifold, i.e. a smooth manifold of steady states for the limiting fast…
Consider an elliptic operator in divergence form with symmetric coefficients.If the diffusion coefficients are periodic, the Bloch theorem allows one to diagonalize the elliptic operator, which is key to the spectral properties of the…
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…
This paper aims to obtain an analytic approximation to the evolution of circular orbits governed by the Earth's $J_2$ and the luni-solar gravitational perturbations. Assuming that the lunar orbital plane coincides with the ecliptic plane,…
The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…
This paper deals with the dynamics of time-reversible Hamiltonian vector fields with 2 and 3 degrees of freedom around an elliptic equilibrium point in presence of symplectic involutions. The main results discuss the existence of…
Although mass transfer (MT) has been studied primarily in circular binaries, observations show that it also occurs in eccentric systems. We investigate orbital evolution during nonconservative MT in eccentric orbits, a process especially…
We present a tidal model for treating the rotational evolution in the general three-body problem with arbitrary viscosities, in which all the masses are considered to be extended and all the tidal interactions between pairs are taken into…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…
The spatial Kepler problem with a perturbation satisfying the rotational symmetry w.r.t. the $z$-axis and the reflection symmetry w.r.t. the $(x, y)$-plane, can be reduced to an Hamiltonian system with 2 degrees of freedom after fixing the…
Finite eccentricities in mass-transferring eccentric binary systems can be explained by taking into account mass-loss and mass-transfer processes that often occur in these systems. These processes can be treated as perturbations to the…
The true- and eccentric-anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits by considering perturbations of the radial part of kinetic energy as a series in the negative powers of the orbital radius. A…
We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…