Heteroclinic Connections Between Periodic Orbits in Planar Restricted Circular Three Body Problem. Part II

We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem (PCR3BP) corresponding to the Sun-Jupiter-Oterma system possesses an infinite number of symmetric periodic orbits and homoclinic orbits to the Lyapunov orbits. Moreover, we show the existence of symbolic dynamics on six symbols for PCR3BP and the possibility of resonance transitions of the comet. This extends earlier results by Wilczak and Zgliczynski [12]. Electronic Supplementary Material: Supplementary material is available in the online version of this article at An erratum to this article is available at .     

Restricted Three Body Problems at the Nanoscale

In this paper, we investigate some of the classical restricted three body problems at the nanoscale, such as the circular planar restricted problem for three C₆₀ fullerenes, and a carbon atom and two C₆₀ fullerenes. We model the van der Waals forces between the fullerenes by the Lennard–Jones potential. In particular, the pairwise potential energies between the carbon atoms on the fullerenes are approximated by the continuous approach, so that the total molecular energy between two fullerenes can be determined analytically. Since we assume that such interactions between the molecules occur at sufficiently large distance, the classical three body problems analysis is legitimate to determine the collective angular velocity of the two and three C₆₀ fullerenes at the nanoscale. We find that the maximum collective angular velocity of the two and three fullerenes systems reach the terahertz range and we also determine the stationary points and the points which have maximum velocity for the carbon atom, for the carbon atom and the two fullerenes system.     

Possibility of Self-Induced Transparency in Multi-Layer Semiconductor Heterostructure Placed in a Quantizing Magnetic Field

The possibility of self-induced transparency is discussed in a semiconductor structure with 3D-quantized electron spectrum. A model structure is proposed, for which a significant decrease of pulse duration and an increase of power is obtained.     

Two-Centre Regularization: One-Dimensional Restricted Four-Body Problem

We consider a two-centre regularization procedure in order to study mainly a one-dimensional restricted four-body problem for charge dynamics. Our particular system is the hydrogen molecule, which is a mixed chaotic system. Several types of periodic orbits of that two-fixed-centre system were found for one-dimensional medial and axial configurations. Permanent address: Departamento de Química, Centro Universitário FIEO (UNIFIEO) Osasco, SP 06020-190, Brazil     

Equilibrium Points in the Restricted Four-Body Problem with Radiation Pressure

This paper studies numerically the photogravitational version of the restricted four-body problem, where an infinitesimal particle is moving under the gravitational attraction and radiation pressure of three bodies much bigger than the particle, the primaries. The fourth body does not affect the motion of the three bodies. These bodies are always at the vertices of an equilateral triangle (Lagrange configuration). We consider all the primary bodies (m ₁, m ₂, m ₃) as radiation sources with radiation factors of the two bodies (m ₂ and m ₃) equal. In this paper we suppose the masses of the three primary bodies are equal. It is found that the involved parameters influenced the positions of the equilibrium points. The linear stability of the relative equilibrium solutions is also studied and all these points are unstable.     

Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem

Symplectic algebraic dynamics algorithm （SADA ） for ordinary differential equations is applied to solve numerically the circular restricted three-body problem （CR3BP） in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge~Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term cMculations of the CR3BP.     

Theoretical Study of the Electronic and Optical Properties of a Heterostructure Based on PTCDA Organic Semiconductor and MoSe2

JETP Letters - The structural and physicochemical properties of the MoSe2/PTCDA heterostructure, which consists of two-dimensional inorganic and molecular organic semiconductors, have been studied...     

Genuine Equilibria of Three Body Coulomb Configurations

The problem analyzed is the classical non-regularized Hamiltonian formulation of a restricted three body problem under the influence of Coulomb-interactions. Completing the large literature on Helium-like systems we will consider the motions around a fixed positive point charge of (i) one negative and one positive point charge as well as the “classical” issue of (ii) two negative point charges. Thereby, all our considerations deal with arbitrary positive and negative charge values of the mass particles. Here, we give necessary and sufficient conditions for the existence of genuine equilibria in such systems—recall that there are none in the usual classical Helium-atom—and analyze their linearized stability. The thus obtained insights allow us to study the dynamics near such genuine equilibria.     

谈“天体问题”中几个疑难问题突破的教学处理

阐述了"天体问题"中三个典型的疑难问题的教学处理.     

The Dynamical Problem for a Rigid Body in Special Relativity

The dynamical problem for a continuous body constrained to undergo only plane BORN motions is solved in special relativity.     

A New Fractional Model for the Falling Body Problem

Recently; a conformable fractional derivative has been proposed to calculate the derivative of non-integer order of time functions. It has been shown that this new fractional derivative definition obeys many advantages over the preceding definitions. For mathematical models in applied sciences and to preserve the dimensionality of the physical quantities, an auxiliary parameter(σ) which has the dimension of seconds should be implemented in the fractional derivative definition. We obtain analytic solutions for the resulting conformable fractional differential equations describing the vertical velocity and the height of the falling body. It is shown that the dimensions of velocity and height are always correct without any restrictions on the auxiliary parameter σ which contradicts with the results in the literature when applying the Caputo definition to the same problem. This may open the door for many future works either to describe the role of such an auxiliary parameter or to derive a more suitable definition for the fractional derivative.     

Periodic Orbits, Symbolic Dynamics and Topological Entropy for the Restricted 3-Body Problem

This paper concerns the restricted 3-body problem. By applying topological methods we give a computer assisted proof of the existence of some classes of periodic orbits, the existence of symbolic dynamics and we give a rigorous lower estimate for the topological entropy. Received: 16 October 2001 / Accepted: 2 February 2002     

Perturbation Theory in the Problem of Light Scattering by a Dielectric Body

In this letter, we describe the observation of a magnetic field dependent electronic gap, suggestive of local superconductivity, in the point-contact spectrum of microcrystalline graphite. Magnetic field dependent point-contact spectroscopy has been carried out at a temperature of 1.8 K using an etched aluminum tip. At zero field, a gap structure in the differential conductance is observed, showing a gap of Δ = 4.2 meV. On applying magnetic fields of up to 500 mT, this gap gradually closes, following the theoretical prediction by Ginzburg and Landau for a fully flux-penetrated superconductor. By applying BCS-theory, we infer a critical superconducting temperature of 14 K.     

多轨道最速落径演示装置

设计制作了基于STC89C52RC单片机的多轨道最速落径演示装置,通过对电磁铁和显示屏的自动控制,将测量数据直接由数码管显示。多轨道对比演示、即时显示数据,达到了直观演示最速落径问题的设计目的。