Related papers: Modeling and dynamics near irregular elongated ast…
We calculate a collective number of thermodynamic quantities in a one-dimensional gas of hard elongated objects (such as needles) whose centers mobile on a line. Our formalism uses an approximation for the probabilities of contact between…
We examine the dynamics of particles around a rotating regular black hole. In particular we focus on the effects of the characteristic length parameter of the spinning black hole on the motion of the particles by solving the equation of…
The space missions designed to visit small bodies of the Solar System boosted the study of the dynamics around non-spherical bodies. In this vein, we study the dynamics around a class of objects classified by us as Non-Spherical Symmetric…
The collapse of non-collisional dark matter and the formation of pancake structures in the Universe are investigated approximately. Collapse is described by a system of ordinary differential equations, in the model of a uniformly rotating,…
We investigate the dynamics of a nonzero mass, circular orbit planet around an eccentric orbit binary for various values of the binary eccentricity, binary mass fraction, planet mass, and planet semi--major axis by means of numerical…
We consider the forced motion of a relativistic particle constrained on a curve and present sufficient conditions for periodic oscillations by means of an illustrative geometrical approach. Obtained result is illustrated by a few examples…
Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital…
The order and chaos of the motion near equilibrium points in the potential of a rotating highly irregular-shaped celestial body are investigated from point of view of the dynamical system theory. The positions of the non-degenerate…
We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lam{\'e} functions that describe the orbits bifurcated from the fundamental linear orbit in…
We explore the complex dynamics of a non-coalescing drop of moderate size inside a circular hydraulic jump of the same liquid formed on a horizontal disk. In this situation the drop is moving along the jump and one observes two different…
We study the dynamics of a quantum or classical particle in a two-dimensional rotating anisotropic harmonic potential. By a sequence of symplectic transformations for constant rotation velocity we find uncoupled normal generalized…
This paper is devoted to a detailed investigation of the perturbed pendulum-like motions of a heavy rigid body about a fixed point. Canonical variables that allow one to simplify the analysis of homoclinic and heteroclinic orbits are…
In this paper we review a recently developed approximate method for investigation of dynamics of compressible ellipsoidal figures. Collapse and subsequent behaviour are described by a system of ordinary differential equations for time…
We aim to understand how landslides affect the shape and rotational motion of small rubble planetary bodies. We limit ourselves to axisymmetric global landslides, and take the primordial shape of the body to also be axisymmetric. The…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
The physical and mathematical properties of the non-linearly coupled black-hole-orbiting-ring system are studied analytically to second order in the dimensionless angular velocity $M_{\text{ir}}\omega_{\text{H}}$ of the black-hole horizon…
We will discuss some specific applications to the rotation state and the shapes of moderately large asteroids, and techniques of observations putting some emphasis on the HST/FGS instrument.
In this report, we present a dynamical systems' approach to study the exact nonlinear wave-particle interaction in relativistic regime. We give a particular attention to the effect of wave obliquity on the dynamics of the orbits by studying…
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…
We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian…