相关论文: Kozai Lidov Cycles = Simple Pendulum
The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in…
One of the simplest models used in studying the dynamics of large-scale structure in cosmology, known as the Zeldovich approximation, is equivalent to the three-dimensional inviscid Burgers equation for potential flow. For smooth initial…
We prove the existence of an almost full measure set of $(3n-2)$--dimensional quasi periodic motions in the planetary problem with $(1+n)$ masses, with eccentricities arbitrarily close to the Levi-Civita limiting value and relatively high…
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…
We report results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg- Landau equation (CGLE) with the cubic-quintic (CQ) combination of gain and loss…
A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other…
A disk around one component of a binary star system with sufficiently high inclination can undergo Kozai-Lidov (KL) oscillations during which the disk inclination and disk eccentricity are exchanged. Previous studies show that without a…
We develop a realistic and analytically tractable model to describe the spin current which arises in a quantum point contact (QPC) with spin-orbit interaction (SOI) upon a small voltage is applied. In the model, the QPC is considered as a…
The semiclassical formula for the quantum propagator in the coherent state representation $<\mathbf{z}'' | e^{-i\hat{H}T/\hbar} | \mathbf{z}'>$ is not free from the problem of caustics. These are singular points along the complex classical…
The nuclear quadrupole collective states at low excitation energies are described in a novel, fully quantum mechanical and systematic manner as compared to traditional pictures initiated by Aage Bohr. The ellipsoidal shapes are shown to be…
In this paper we answer a simple question: can a misaligned circumbinary planet induce Kozai-Lidov cycles on an inner stellar binary? We use known analytic equations to analyse the behaviour of the Kozai-Lidov effect as the outer mass is…
A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by…
In galactic nuclei, the gravitational potential is dominated by the central supermassive black hole, so stars follow quasi-Keplerian orbits. These orbits are distorted by gravitational forces from other stars, leading to long-term orbital…
The rosette-shaped motion of a particle in a central force field is known to be classically solvable by quadratures. We present a new approach of describing and characterizing such motion based on the eccentricity vector of the two body…
Consider the spatial restricted three-body problem, as a model for the motion of a spacecraft relative to the Sun-Earth system. We focus on the dynamics near the equilibrium point $L_1$, located between the Sun and the Earth. We show that…
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…
We have presented a complete description of classical dynamics generated by the Hamiltonian of quadrupole nuclear oscillations and identified those peculiarities of quantum dynamics that can be interpreted as quantum manifestations of…
In recent years many binary minor planets (BMPs) have been discovered in the Solar system. Many models have been suggested for their formation, but these encounter difficulties explaining their observed characteristics. Here we show that…
Simple cosmological models based upon five-dimensional Kaluza-Klein relativity are re-examined and interesting properties are indicated. These models are special cases of those obtained by Davidson et al. and Mann and Vincent, specifically,…
The effect of an octupole term in a quadrupole deformed single particle potential is studied from the classical and quantum mechanical view point. Whereas the problem is nonintegrable, the quantum mechanical spectrum nevertheless shows some…